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 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$$m$) 11B57 Farey sequences; the sequences ${1^k, 2^k, \cdots}$${1^k, 2^k, \cdots}$ 11B65 Binomial coefficients; factorials; $q$$q$-identities [See also 05A10, 05A30] 11B68 Bernoulli and Euler numbers and polynomials 11B73 Bell and Stirling numbers 11B75 Other combinatorial number theory 11B83 Special sequences and polynomials 11B85 Automata sequences 11B99 None of the above, but in this section 11C08 Polynomials [See also 13F20] 11C20 Matrices, determinants [See also 15A36] 11C99 None of the above, but in this section 11D04 Linear equations 11D09 Quadratic and bilinear equations 11D25 Cubic and quartic equations 11D41 Higher degree equations; Fermat's equation 11D45 Counting solutions of Diophantine equations 11D57 Multiplicative and norm form equations 11D59 Thue-Mahler equations 11D61 Exponential equations 11D68 Rational numbers as sums of fractions 11D72 Equations in many variables [See also 11P55] 11D75 Diophantine inequalities [See also 11J25] 11D79 Congruences in many variables 11D85 Representation problems [See also 11P55] 11D88 $p$$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$$K$-theory of quadratic and Hermitian forms 11E72 Galois cohomology of linear algebraic groups [See also 20G10] 11E76 Forms of degree higher than two 11E81 Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24] 11E88 Quadratic spaces; Clifford algebras [See also 15A63, 15A66] 11E95 $p$$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$$p$-adic modular forms [See also 14G20, 22E50] 11F37 Forms of half-integer weight; nonholomorphic modular forms 11F41 Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20] 11F46 Siegel modular groups and their modular and automorphic forms 11F50 Jacobi forms 11F52 Modular forms associated to Drinfelʹd modules 11F55 Other groups and their modular and automorphic forms (several variables) 11F60 Hecke-Petersson operators, differential operators (several variables) 11F66 Dirichlet series and functional equations in connection with modular forms 11F67 Special values of automorphic $L$$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$$p$-adic theory, local fields [See also 14G20, 22E50] 11F99 None of the above, but in this section 11G05 Elliptic curves over global fields [See also 14H52] 11G07 Elliptic curves over local fields [See also 14G20, 14H52] 11G09 Drinfelʹd modules; higher-dimensional motives, etc. [See also 14L05] 11G10 Abelian varieties of dimension $\gtr 1$$\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$$\ne 1$ over global fields [See also 14H25] 11G35 Varieties over global fields [See also 14G25] 11G40 $L$$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$$K$-theory 11G99 None of the above, but in this section 11H06 Lattices and convex bodies [See also 11P21, 52C05, 52C07] 11H16 Nonconvex bodies 11H31 Lattice packing and covering [See also 05B40, 52C15, 52C17] 11H46 Products of linear forms 11H50 Minima of forms 11H55 Quadratic forms (reduction theory, extreme forms, etc.) 11H56 Automorphism groups of lattices 11H60 Mean value and transfer theorems 11H71 Relations with coding theory 11H99 None of the above, but in this section 11J04 Homogeneous approximation to one number 11J06 Markov and Lagrange spectra and generalizations 11J13 Simultaneous homogeneous approximation, linear forms 11J17 Approximation by numbers from a fixed field 11J20 Inhomogeneous linear forms 11J25 Diophantine inequalities [See also 11D75] 11J54 Small fractional parts of polynomials and generalizations 11J61 Approximation in non-Archimedean valuations 11J68 Approximation to algebraic numbers 11J70 Continued fractions and generalizations [See also 11A55, 11K50] 11J71 Distribution modulo one [See also 11K06] 11J72 Irrationality; linear independence over a field 11J81 Transcendence (general theory) 11J82 Measures of irrationality and of transcendence 11J83 Metric theory 11J85 Algebraic independence; Gelʹfond's method 11J86 Linear forms in logarithms; Baker's method 11J89 Transcendence theory of elliptic and abelian functions 11J91 Transcendence theory of other special functions 11J93 Transcendence theory of Drinfelʹd and $t$$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$$1$ [See also 11J71] 11K16 Normal numbers, radix expansions, etc. [See also 11A63] 11K31 Special sequences 11K36 Well-distributed sequences and other variations 11K38 Irregularities of distribution, discrepancy [See also 11Nxx] 11K41 Continuous, $p$$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)$$\zeta (s)$ and $L(s, \chi)$$L(s, \chi)$ 11M20 Real zeros of $L(s, \chi)$$L(s, \chi)$; results on $L(1, \chi)$$L(1, \chi)$ 11M26 Nonreal zeros of $\zeta (s)$$\zeta (s)$ and $L(s, \chi)$$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$$L$-functions in characteristic $p$$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$$L$-functions of number fields [See also 11M41, 19F27] 11R44 Distribution of prime ideals [See also 11N05] 11R45 Density theorems 11R47 Other analytic theory [See also 11Nxx] 11R52 Quaternion and other division algebras: arithmetic, zeta functions 11R54 Other algebras and orders, and their zeta and $L$$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$$K$-theory of global fields [See also 19Fxx] 11R80 Totally real and totally positive fields [See also 12J15] 11R99 None of the above, but in this section 11S05 Polynomials 11S15 Ramification and extension theory 11S20 Galois theory 11S23 Integral representations 11S25 Galois cohomology [See also 12Gxx, 16H05] 11S31 Class field theory; $p$$p$-adic formal groups [See also 14L05] 11S37 Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50] 11S40 Zeta functions and $L$$L$-functions [See also 11M41, 19F27] 11S45 Algebras and orders, and their zeta functions [See also 11R52, 11R54, 16H05, 16Kxx] 11S70 $K$$K$-theory of local fields [See also 19Fxx] 11S80 Other analytic theory (analogues of beta and gamma functions, $p$$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
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