11-XX |
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|
Number theory |
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11-00 |
General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to number theory |
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11-01 |
Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory |
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11-02 |
Research exposition (monographs, survey articles) pertaining to number theory |
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11-03 |
History of number theory [Consider also classification numbers from Section 01-XX] |
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11-04 |
Software, source code, etc. for problems pertaining to number theory |
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11-06 |
Proceedings, conferences, collections, etc. pertaining to number theory |
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11A05 |
Multiplicative structure; Euclidean algorithm; greatest common divisors |
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11A07 |
Congruences; primitive roots; residue systems |
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11A15 |
Power residues, reciprocity |
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11A25 |
Arithmetic functions; related numbers; inversion formulas |
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11A41 |
Primes |
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11A51 |
Factorization; primality |
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11A55 |
Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15] |
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11A63 |
Radix representation; digital problems {For metric results, see 11K16} |
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11A67 |
Other number representations |
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11A99 |
None of the above, but in this section |
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11B05 |
Density, gaps, topology |
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11B13 |
Additive bases, including sumsets [See also 05B10] |
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11B25 |
Arithmetic progressions [See also 11N13] |
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11B30 |
Arithmetic combinatorics; higher degree uniformity |
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11B34 |
Representation functions |
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11B37 |
Recurrences {For applications to special functions, see 33-XX} |
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11B39 |
Fibonacci and Lucas numbers and polynomials and generalizations |
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11B50 |
Sequences (mod $m$) |
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11B57 |
Farey sequences; the sequences $1^k, 2^k, \dots$ |
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11B65 |
Binomial coefficients; factorials; $q$-identities [See also 05A10, 05A30] |
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11B68 |
Bernoulli and Euler numbers and polynomials |
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11B73 |
Bell and Stirling numbers |
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11B75 |
Other combinatorial number theory |
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11B83 |
Special sequences and polynomials |
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11B85 |
Automata sequences |
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11B99 |
None of the above, but in this section |
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11C08 |
Polynomials in number theory [See also 13F20] |
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11C20 |
Matrices, determinants in number theory [See also 15B36] |
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11C99 |
None of the above, but in this section |
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11D04 |
Linear Diophantine equations |
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11D07 |
The Frobenius problem |
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11D09 |
Quadratic and bilinear Diophantine equations |
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11D25 |
Cubic and quartic Diophantine equations |
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11D41 |
Higher degree equations; Fermat's equation |
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11D45 |
Counting solutions of Diophantine equations |
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11D57 |
Multiplicative and norm form equations |
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11D59 |
Thue-Mahler equations |
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11D61 |
Exponential Diophantine equations |
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11D68 |
Rational numbers as sums of fractions |
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11D72 |
Diophantine equations in many variables [See also 11P55] |
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11D75 |
Diophantine inequalities [See also 11J25] |
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11D79 |
Congruences in many variables |
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11D85 |
Representation problems [See also 11P55] |
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11D88 |
$p$-adic and power series fields |
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11D99 |
None of the above, but in this section |
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11E04 |
Quadratic forms over general fields |
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11E08 |
Quadratic forms over local rings and fields |
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11E10 |
Forms over real fields |
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11E12 |
Quadratic forms over global rings and fields |
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11E16 |
General binary quadratic forms |
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11E20 |
General ternary and quaternary quadratic forms; forms of more than two variables |
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11E25 |
Sums of squares and representations by other particular quadratic forms |
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11E39 |
Bilinear and Hermitian forms |
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11E41 |
Class numbers of quadratic and Hermitian forms |
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11E45 |
Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) |
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11E57 |
Classical groups [See also 14Lxx, 20Gxx] |
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11E70 |
$K$-theory of quadratic and Hermitian forms |
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11E72 |
Galois cohomology of linear algebraic groups [See also 20G10] |
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11E76 |
Forms of degree higher than two |
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11E81 |
Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24] |
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11E88 |
Quadratic spaces; Clifford algebras [See also 15A63, 15A66] |
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11E95 |
$p$-adic theory |
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11E99 |
None of the above, but in this section |
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11F03 |
Modular and automorphic functions |
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11F06 |
Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40] |
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11F11 |
Holomorphic modular forms of integral weight |
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11F12 |
Automorphic forms, one variable |
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11F20 |
Dedekind eta function, Dedekind sums |
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11F22 |
Relationship to Lie algebras and finite simple groups |
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11F23 |
Relations with algebraic geometry and topology |
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11F25 |
Hecke-Petersson operators, differential operators (one variable) |
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11F27 |
Theta series; Weil representation; theta correspondences |
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11F30 |
Fourier coefficients of automorphic forms |
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11F32 |
Modular correspondences, etc. |
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11F33 |
Congruences for modular and $p$-adic modular forms |
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11F37 |
Forms of half-integer weight; nonholomorphic modular forms |
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11F41 |
Automorphic forms on $\mbox{GL}(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14G35] |
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11F46 |
Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms |
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11F50 |
Jacobi forms |
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11F52 |
Modular forms associated to Drinfel'd modules |
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11F55 |
Other groups and their modular and automorphic forms (several variables) |
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11F60 |
Hecke-Petersson operators, differential operators (several variables) |
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11F66 |
Langlands $L$-functions; one variable Dirichlet series and functional equations |
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11F67 |
Special values of automorphic $L$-series, periods of automorphic forms, cohomology, modular symbols |
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11F68 |
Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series |
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11F70 |
Representation-theoretic methods; automorphic representations over local and global fields |
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11F72 |
Spectral theory; trace formulas (e.g., that of Selberg) |
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11F75 |
Cohomology of arithmetic groups |
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11F80 |
Galois representations |
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11F85 |
$p$-adic theory, local fields [See also 14G20, 22E50] |
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11F99 |
None of the above, but in this section |
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11G05 |
Elliptic curves over global fields [See also 14H52] |
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11G07 |
Elliptic curves over local fields [See also 14G20, 14H52] |
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11G09 |
Drinfel'd modules; higher-dimensional motives, etc. [See also 14L05] |
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11G10 |
Abelian varieties of dimension $> 1$ [See also 14Kxx] |
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11G15 |
Complex multiplication and moduli of abelian varieties [See also 14K22] |
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11G16 |
Elliptic and modular units [See also 11R27] |
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11G18 |
Arithmetic aspects of modular and Shimura varieties [See also 14G35] |
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11G20 |
Curves over finite and local fields [See also 14H25] |
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11G25 |
Varieties over finite and local fields [See also 14G15, 14G20] |
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11G30 |
Curves of arbitrary genus or genus $\ne 1$ over global fields [See also 14H25] |
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11G32 |
Arithmetic aspects of dessins d'enfants, Belyĭ theory |
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11G35 |
Varieties over global fields [See also 14G25] |
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11G40 |
$L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10] |
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11G42 |
Arithmetic mirror symmetry [See also 14J33] |
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11G45 |
Geometric class field theory [See also 11R37, 14C35, 19F05] |
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11G50 |
Heights [See also 14G40, 37P30] |
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11G55 |
Polylogarithms and relations with $K$-theory |
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11G99 |
None of the above, but in this section |
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11H06 |
Lattices and convex bodies (number-theoretic aspects) [See also 11P21, 52C05, 52C07] |
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11H16 |
Nonconvex bodies |
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11H31 |
Lattice packing and covering (number-theoretic aspects) [See also 05B40, 52C15, 52C17] |
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11H46 |
Products of linear forms |
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11H50 |
Minima of forms |
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11H55 |
Quadratic forms (reduction theory, extreme forms, etc.) |
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11H56 |
Automorphism groups of lattices |
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11H60 |
Mean value and transfer theorems |
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11H71 |
Relations with coding theory |
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11H99 |
None of the above, but in this section |
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11J04 |
Homogeneous approximation to one number |
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11J06 |
Markov and Lagrange spectra and generalizations |
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11J13 |
Simultaneous homogeneous approximation, linear forms |
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11J17 |
Approximation by numbers from a fixed field |
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11J20 |
Inhomogeneous linear forms |
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11J25 |
Diophantine inequalities [See also 11D75] |
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11J54 |
Small fractional parts of polynomials and generalizations |
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11J61 |
Approximation in non-Archimedean valuations |
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11J68 |
Approximation to algebraic numbers |
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11J70 |
Continued fractions and generalizations [See also 11A55, 11K50] |
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11J71 |
Distribution modulo one [See also 11K06] |
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11J72 |
Irrationality; linear independence over a field |
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11J81 |
Transcendence (general theory) |
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11J82 |
Measures of irrationality and of transcendence |
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11J83 |
Metric theory |
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11J85 |
Algebraic independence; Gel'fond's method |
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11J86 |
Linear forms in logarithms; Baker's method |
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11J87 |
Schmidt Subspace Theorem and applications |
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11J89 |
Transcendence theory of elliptic and abelian functions |
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11J91 |
Transcendence theory of other special functions |
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11J93 |
Transcendence theory of Drinfel'd and $t$-modules |
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11J95 |
Results involving abelian varieties |
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11J97 |
Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.) |
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11J99 |
None of the above, but in this section |
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11K06 |
General theory of distribution modulo $1$ [See also 11J71] |
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11K16 |
Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63] |
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11K31 |
Special sequences |
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11K36 |
Well-distributed sequences and other variations |
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11K38 |
Irregularities of distribution, discrepancy [See also 11Nxx] |
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11K41 |
Continuous, $p$-adic and abstract analogues |
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11K45 |
Pseudo-random numbers; Monte Carlo methods [See also 65C05, 65C10] |
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11K50 |
Metric theory of continued fractions [See also 11A55, 11J70] |
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11K55 |
Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx] |
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11K60 |
Diophantine approximation in probabilistic number theory [See also 11Jxx] |
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11K65 |
Arithmetic functions in probabilistic number theory [See also 11Nxx] |
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11K70 |
Harmonic analysis and almost periodicity in probabilistic number theory |
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11K99 |
None of the above, but in this section |
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11L03 |
Trigonometric and exponential sums (general theory) |
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11L05 |
Gauss and Kloosterman sums; generalizations |
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11L07 |
Estimates on exponential sums |
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11L10 |
Jacobsthal and Brewer sums; other complete character sums |
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11L15 |
Weyl sums |
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11L20 |
Sums over primes |
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11L26 |
Sums over arbitrary intervals |
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11L40 |
Estimates on character sums |
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11L99 |
None of the above, but in this section |
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11M06 |
$\zeta (s)$ and $L(s, \chi)$ |
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11M20 |
Real zeros of $L(s, \chi)$; results on $L(1, \chi)$ |
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11M26 |
Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses |
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11M32 |
Multiple Dirichlet series and zeta functions and multizeta values |
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11M35 |
Hurwitz and Lerch zeta functions |
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11M36 |
Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) |
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11M38 |
Zeta and $L$-functions in characteristic $p$ |
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11M41 |
Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10} [See also 11E45, 11F66, 11F70, 11F72] |
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11M45 |
Tauberian theorems [See also 40E05] |
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11M50 |
Relations with random matrices |
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11M55 |
Relations with noncommutative geometry |
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11M99 |
None of the above, but in this section |
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11N05 |
Distribution of primes |
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11N13 |
Primes in congruence classes |
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11N25 |
Distribution of integers with specified multiplicative constraints |
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11N30 |
Turán theory [See also 30Bxx] |
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11N32 |
Primes represented by polynomials; other multiplicative structures of polynomial values |
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11N35 |
Sieves |
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11N36 |
Applications of sieve methods |
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11N37 |
Asymptotic results on arithmetic functions |
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11N45 |
Asymptotic results on counting functions for algebraic and topological structures |
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11N56 |
Rate of growth of arithmetic functions |
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11N60 |
Distribution functions associated with additive and positive multiplicative functions |
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11N64 |
Other results on the distribution of values or the characterization of arithmetic functions |
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11N69 |
Distribution of integers in special residue classes |
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11N75 |
Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx] |
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11N80 |
Generalized primes and integers |
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11N99 |
None of the above, but in this section |
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11P05 |
Waring's problem and variants |
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11P21 |
Lattice points in specified regions |
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11P32 |
Goldbach-type theorems; other additive questions involving primes |
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11P55 |
Applications of the Hardy-Littlewood method [See also 11D85] |
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11P70 |
Inverse problems of additive number theory, including sumsets |
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11P81 |
Elementary theory of partitions [See also 05A17] |
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11P82 |
Analytic theory of partitions |
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11P83 |
Partitions; congruences and congruential restrictions |
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11P84 |
Partition identities; identities of Rogers-Ramanujan type |
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11P99 |
None of the above, but in this section |
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11R04 |
Algebraic numbers; rings of algebraic integers |
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11R06 |
PV-numbers and generalizations; other special algebraic numbers; Mahler measure |
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11R09 |
Polynomials (irreducibility, etc.) |
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11R11 |
Quadratic extensions |
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11R16 |
Cubic and quartic extensions |
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11R18 |
Cyclotomic extensions |
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11R20 |
Other abelian and metabelian extensions |
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11R21 |
Other number fields |
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11R23 |
Iwasawa theory |
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11R27 |
Units and factorization |
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11R29 |
Class numbers, class groups, discriminants |
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11R32 |
Galois theory |
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11R33 |
Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10] |
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11R34 |
Galois cohomology [See also 12Gxx, 19F05] |
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11R37 |
Class field theory |
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11R39 |
Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55] |
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11R42 |
Zeta functions and $L$-functions of number fields [See also 11M41, 19F27] |
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11R44 |
Distribution of prime ideals [See also 11N05] |
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11R45 |
Density theorems |
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11R47 |
Other analytic theory [See also 11Nxx] |
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11R52 |
Quaternion and other division algebras: arithmetic, zeta functions |
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11R54 |
Other algebras and orders, and their zeta and $L$-functions [See also 11S45, 16Hxx] |
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11R56 |
Adèle rings and groups |
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11R58 |
Arithmetic theory of algebraic function fields [See also 14Gxx, 14H05] |
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11R60 |
Cyclotomic function fields (class groups, Bernoulli objects, etc.) |
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11R65 |
Class groups and Picard groups of orders |
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11R70 |
$K$-theory of global fields [See also 19Fxx] |
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11R80 |
Totally real fields [See also 12J15] |
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11R99 |
None of the above, but in this section |
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11S05 |
Polynomials |
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11S15 |
Ramification and extension theory |
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11S20 |
Galois theory |
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11S23 |
Integral representations |
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11S25 |
Galois cohomology [See also 12Gxx, 16H05] |
|
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11S31 |
Class field theory; $p$-adic formal groups [See also 14L05] |
|
|
11S37 |
Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50] |
|
|
11S40 |
Zeta functions and $L$-functions [See also 11M41, 19F27] |
|
|
11S45 |
Algebras and orders, and their zeta functions [See also 11R52, 11R54, 16Hxx, 16Kxx] |
|
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11S70 |
$K$-theory of local fields [See also 19Fxx] |
|
|
11S80 |
Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.) |
|
|
11S82 |
Non-Archimedean dynamical systems [See mainly 37Pxx] |
|
|
11S85 |
Other nonanalytic theory |
|
|
11S90 |
Prehomogeneous vector spaces |
|
|
11S99 |
None of the above, but in this section |
|
|
11T06 |
Polynomials over finite fields |
|
|
11T22 |
Cyclotomy |
|
|
11T23 |
Exponential sums |
|
|
11T24 |
Other character sums and Gauss sums |
|
|
11T30 |
Structure theory for finite fields and commutative rings (number-theoretic aspects) |
|
|
11T55 |
Arithmetic theory of polynomial rings over finite fields |
|
|
11T60 |
Finite upper half-planes |
|
|
11T71 |
Algebraic coding theory; cryptography (number-theoretic aspects) |
|
|
11T99 |
None of the above, but in this section |
|
|
11U05 |
Decidability (number-theoretic aspects) [See also 03B25] |
|
|
11U07 |
Ultraproducts (number-theoretic aspects) [See also 03C20] |
|
|
11U09 |
Model theory (number-theoretic aspects) [See also 03Cxx] |
|
|
11U10 |
Nonstandard arithmetic (number-theoretic aspects) [See also 03H15] |
|
|
11U99 |
None of the above, but in this section |
|
|
11Y05 |
Factorization |
|
|
11Y11 |
Primality |
|
|
11Y16 |
Number-theoretic algorithms; complexity [See also 68Q25] |
|
|
11Y35 |
Analytic computations |
|
|
11Y40 |
Algebraic number theory computations |
|
|
11Y50 |
Computer solution of Diophantine equations |
|
|
11Y55 |
Calculation of integer sequences |
|
|
11Y60 |
Evaluation of number-theoretic constants |
|
|
11Y65 |
Continued fraction calculations (number-theoretic aspects) |
|
|
11Y70 |
Values of arithmetic functions; tables |
|
|
11Y99 |
None of the above, but in this section |
|
|
11Z05 |
Miscellaneous applications of number theory |
|
|
11Z99 |
None of the above, but in this section |