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< 08-XX | Up | 12-XX >
11-XX Number theory
11-00   General reference works (handbooks, dictionaries, bibliographies, etc.)
11-01   Instructional exposition (textbooks, tutorial papers, etc.)
11-02   Research exposition (monographs, survey articles)
11-03   Historical (must also be assigned at least one classification number from Section 01)
11-04   Explicit machine computation and programs (not the theory of computation or programming)
11-06   Proceedings, conferences, collections, etc.
11A05   Multiplicative structure; Euclidean algorithm; greatest common divisors
11A07   Congruences; primitive roots; residue systems
11A15   Power residues, reciprocity
11A25   Arithmetic functions; related numbers; inversion formulas
11A41   Primes
11A51   Factorization; primality
11A55   Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15]
11A63   Radix representation; digital problems {For metric results, see 11K16}
11A67   Other representations
11A99   None of the above, but in this section
11B05   Density, gaps, topology
11B13   Additive bases [See also 05B10]
11B25   Arithmetic progressions [See also 11N13]
11B34   Representation functions
11B37   Recurrences {For applications to special functions, see 33-XX}
11B39   Fibonacci and Lucas numbers and polynomials and generalizations
11B50   Sequences (mod $m$)
11B57   Farey sequences; the sequences ${1^k, 2^k, \cdots}$
11B65   Binomial coefficients; factorials; $q$-identities [See also 05A10, 05A30]
11B68   Bernoulli and Euler numbers and polynomials
11B73   Bell and Stirling numbers
11B75   Other combinatorial number theory
11B83   Special sequences and polynomials
11B85   Automata sequences
11B99   None of the above, but in this section
11C08   Polynomials [See also 13F20]
11C20   Matrices, determinants [See also 15A36]
11C99   None of the above, but in this section
11D04   Linear equations
11D09   Quadratic and bilinear equations
11D25   Cubic and quartic equations
11D41   Higher degree equations; Fermat's equation
11D45   Counting solutions of Diophantine equations
11D57   Multiplicative and norm form equations
11D59   Thue-Mahler equations
11D61   Exponential equations
11D68   Rational numbers as sums of fractions
11D72   Equations in many variables [See also 11P55]
11D75   Diophantine inequalities [See also 11J25]
11D79   Congruences in many variables
11D85   Representation problems [See also 11P55]
11D88   $p$-adic and power series fields
11D99   None of the above, but in this section
11E04   Quadratic forms over general fields
11E08   Quadratic forms over local rings and fields
11E10   Forms over real fields
11E12   Quadratic forms over global rings and fields
11E16   General binary quadratic forms
11E20   General ternary and quaternary quadratic forms; forms of more than two variables
11E25   Sums of squares and representations by other particular quadratic forms
11E39   Bilinear and Hermitian forms
11E41   Class numbers of quadratic and Hermitian forms
11E45   Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)
11E57   Classical groups [See also 14Lxx, 20Gxx]
11E70   $K$-theory of quadratic and Hermitian forms
11E72   Galois cohomology of linear algebraic groups [See also 20G10]
11E76   Forms of degree higher than two
11E81   Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]
11E88   Quadratic spaces; Clifford algebras [See also 15A63, 15A66]
11E95   $p$-adic theory
11E99   None of the above, but in this section
11F03   Modular and automorphic functions
11F06   Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40]
11F11   Modular forms, one variable
11F12   Automorphic forms, one variable
11F20   Dedekind eta function, Dedekind sums
11F22   Relationship to Lie algebras and finite simple groups
11F23   Relations with algebraic geometry and topology
11F25   Hecke-Petersson operators, differential operators (one variable)
11F27   Theta series; Weil representation
11F30   Fourier coefficients of automorphic forms
11F32   Modular correspondences, etc.
11F33   Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]
11F37   Forms of half-integer weight; nonholomorphic modular forms
11F41   Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
11F46   Siegel modular groups and their modular and automorphic forms
11F50   Jacobi forms
11F52   Modular forms associated to Drinfelʹd modules
11F55   Other groups and their modular and automorphic forms (several variables)
11F60   Hecke-Petersson operators, differential operators (several variables)
11F66   Dirichlet series and functional equations in connection with modular forms
11F67   Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
11F70   Representation-theoretic methods; automorphic representations over local and global fields
11F72   Spectral theory; Selberg trace formula
11F75   Cohomology of arithmetic groups
11F80   Galois representations
11F85   $p$-adic theory, local fields [See also 14G20, 22E50]
11F99   None of the above, but in this section
11G05   Elliptic curves over global fields [See also 14H52]
11G07   Elliptic curves over local fields [See also 14G20, 14H52]
11G09   Drinfelʹd modules; higher-dimensional motives, etc. [See also 14L05]
11G10   Abelian varieties of dimension $\gtr 1$ [See also 14Kxx]
11G15   Complex multiplication and moduli of abelian varieties [See also 14K22]
11G16   Elliptic and modular units [See also 11R27]
11G18   Arithmetic aspects of modular and Shimura varieties [See also 14G35]
11G20   Curves over finite and local fields [See also 14H25]
11G25   Varieties over finite and local fields [See also 14G15, 14G20]
11G30   Curves of arbitrary genus or genus $\ne 1$ over global fields [See also 14H25]
11G35   Varieties over global fields [See also 14G25]
11G40   $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]
11G45   Geometric class field theory [See also 11R37, 14C35, 19F05]
11G50   Heights [See also 14G40]
11G55   Polylogarithms and relations with $K$-theory
11G99   None of the above, but in this section
11H06   Lattices and convex bodies [See also 11P21, 52C05, 52C07]
11H16   Nonconvex bodies
11H31   Lattice packing and covering [See also 05B40, 52C15, 52C17]
11H46   Products of linear forms
11H50   Minima of forms
11H55   Quadratic forms (reduction theory, extreme forms, etc.)
11H56   Automorphism groups of lattices
11H60   Mean value and transfer theorems
11H71   Relations with coding theory
11H99   None of the above, but in this section
11J04   Homogeneous approximation to one number
11J06   Markov and Lagrange spectra and generalizations
11J13   Simultaneous homogeneous approximation, linear forms
11J17   Approximation by numbers from a fixed field
11J20   Inhomogeneous linear forms
11J25   Diophantine inequalities [See also 11D75]
11J54   Small fractional parts of polynomials and generalizations
11J61   Approximation in non-Archimedean valuations
11J68   Approximation to algebraic numbers
11J70   Continued fractions and generalizations [See also 11A55, 11K50]
11J71   Distribution modulo one [See also 11K06]
11J72   Irrationality; linear independence over a field
11J81   Transcendence (general theory)
11J82   Measures of irrationality and of transcendence
11J83   Metric theory
11J85   Algebraic independence; Gelʹfond's method
11J86   Linear forms in logarithms; Baker's method
11J89   Transcendence theory of elliptic and abelian functions
11J91   Transcendence theory of other special functions
11J93   Transcendence theory of Drinfelʹd and $t$-modules
11J95   Results involving abelian varieties
11J97   Analogues of methods in Nevanlinna theory (work of Vojta et al.)
11J99   None of the above, but in this section
11K06   General theory of distribution modulo $1$ [See also 11J71]
11K16   Normal numbers, radix expansions, etc. [See also 11A63]
11K31   Special sequences
11K36   Well-distributed sequences and other variations
11K38   Irregularities of distribution, discrepancy [See also 11Nxx]
11K41   Continuous, $p$-adic and abstract analogues
11K45   Pseudo-random numbers; Monte Carlo methods
11K50   Metric theory of continued fractions [See also 11A55, 11J70]
11K55   Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]
11K60   Diophantine approximation [See also 11Jxx]
11K65   Arithmetic functions [See also 11Nxx]
11K70   Harmonic analysis and almost periodicity
11K99   None of the above, but in this section
11L03   Trigonometric and exponential sums, general
11L05   Gauss and Kloosterman sums; generalizations
11L07   Estimates on exponential sums
11L10   Jacobsthal and Brewer sums; other complete character sums
11L15   Weyl sums
11L20   Sums over primes
11L26   Sums over arbitrary intervals
11L40   Estimates on character sums
11L99   None of the above, but in this section
11M06   $\zeta (s)$ and $L(s, \chi)$
11M20   Real zeros of $L(s, \chi)$; results on $L(1, \chi)$
11M26   Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
11M35   Hurwitz and Lerch zeta functions
11M36   Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas
11M38   Zeta and $L$-functions in characteristic $p$
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}
11M45   Tauberian theorems [See also 40E05]
11M99   None of the above, but in this section
11N05   Distribution of primes
11N13   Primes in progressions [See also 11B25]
11N25   Distribution of integers with specified multiplicative constraints
11N30   Turán theory [See also 30Bxx]
11N32   Primes represented by polynomials; other multiplicative structure of polynomial values
11N35   Sieves
11N36   Applications of sieve methods
11N37   Asymptotic results on arithmetic functions
11N45   Asymptotic results on counting functions for algebraic and topological structures
11N56   Rate of growth of arithmetic functions
11N60   Distribution functions associated with additive and positive multiplicative functions
11N64   Other results on the distribution of values or the characterization of arithmetic functions
11N69   Distribution of integers in special residue classes
11N75   Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx]
11N80   Generalized primes and integers
11N99   None of the above, but in this section
11P05   Waring's problem and variants
11P21   Lattice points in specified regions
11P32   Goldbach-type theorems; other additive questions involving primes
11P55   Applications of the Hardy-Littlewood method [See also 11D85]
11P70   Inverse problems of additive number theory
11P81   Elementary theory of partitions [See also 05A17]
11P82   Analytic theory of partitions
11P83   Partitions; congruences and congruential restrictions
11P99   None of the above, but in this section
11R04   Algebraic numbers; rings of algebraic integers
11R06   PV-numbers and generalizations; other special algebraic numbers
11R09   Polynomials (irreducibility, etc.)
11R11   Quadratic extensions
11R16   Cubic and quartic extensions
11R18   Cyclotomic extensions
11R20   Other abelian and metabelian extensions
11R21   Other number fields
11R23   Iwasawa theory
11R27   Units and factorization
11R29   Class numbers, class groups, discriminants
11R32   Galois theory
11R33   Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10]
11R34   Galois cohomology [See also 12Gxx, 16H05, 19A31]
11R37   Class field theory
11R39   Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]
11R42   Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]
11R44   Distribution of prime ideals [See also 11N05]
11R45   Density theorems
11R47   Other analytic theory [See also 11Nxx]
11R52   Quaternion and other division algebras: arithmetic, zeta functions
11R54   Other algebras and orders, and their zeta and $L$-functions [See also 11S45, 16H05, 16Kxx]
11R56   Adèle rings and groups
11R58   Arithmetic theory of algebraic function fields [See also 14-XX]
11R60   Cyclotomic function fields (class groups, Bernoulli objects, etc.)
11R65   Class groups and Picard groups of orders
11R70   $K$-theory of global fields [See also 19Fxx]
11R80   Totally real and totally positive fields [See also 12J15]
11R99   None of the above, but in this section
11S05   Polynomials
11S15   Ramification and extension theory
11S20   Galois theory
11S23   Integral representations
11S25   Galois cohomology [See also 12Gxx, 16H05]
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, 16H05, 16Kxx]
11S70   $K$-theory of local fields [See also 19Fxx]
11S80   Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.)
11S85   Other nonanalytic theory
11S90   Prehomogeneous vector spaces
11S99   None of the above, but in this section
11T06   Polynomials
11T22   Cyclotomy
11T23   Exponential sums
11T24   Other character sums and Gauss sums
11T30   Structure theory
11T55   Arithmetic theory of polynomial rings over finite fields
11T60   Finite upper half-planes
11T71   Algebraic coding theory; cryptography
11T99   None of the above, but in this section
11U05   Decidability [See also 03B25]
11U07   Ultraproducts [See also 03C20]
11U09   Model theory [See also 03Cxx]
11U10   Nonstandard arithmetic [See also 03H15]
11U99   None of the above, but in this section
11Y05   Factorization
11Y11   Primality
11Y16   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 constants
11Y65   Continued fraction calculations
11Y70   Values of arithmetic functions; tables
11Y99   None of the above, but in this section
11Z05   Miscellaneous applications of number theory
< 08-XX | Up | 12-XX >
 
 
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