11XX 


Number theory 


1100 
General reference works (handbooks, dictionaries, bibliographies, etc.) 


1101 
Instructional exposition (textbooks, tutorial papers, etc.) 


1102 
Research exposition (monographs, survey articles) 


1103 
Historical (must also be assigned at least one classification number from Section 01) 


1104 
Explicit machine computation and programs (not the theory of computation or programming) 


1106 
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, including sumsets [See also 05B10] 


11B25 
Arithmetic progressions [See also 11N13] 


11B30 
Arithmetic combinatorics; higher degree uniformity 


11B34 
Representation functions 


11B37 
Recurrences {For applications to special functions, see 33XX} 


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 15B36] 


11C99 
None of the above, but in this section 


11D04 
Linear equations 


11D07 
The Frobenius problem 


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 
ThueMahler 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 
Holomorphic modular forms of integral weight 


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 
HeckePetersson operators, differential operators (one variable) 


11F27 
Theta series; Weil representation; theta correspondences 


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 halfinteger weight; nonholomorphic modular forms 


11F41 
Automorphic forms on ${\rm GL}(2)$; Hilbert and HilbertSiegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20] 


11F46 
Siegel modular groups; Siegel and HilbertSiegel 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 
HeckePetersson operators, differential operators (several variables) 


11F66 
Langlands $L$functions; one variable Dirichlet series and functional equations 


11F67 
Special values of automorphic $L$series, periods of modular forms, cohomology, modular symbols 


11F68 
Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series 


11F70 
Representationtheoretic 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; higherdimensional motives, etc. [See also 14L05] 


11G10 
Abelian varieties of dimension $> 1$ [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] 


11G32 
Dessins d'enfants, Belyĭ theory 


11G35 
Varieties over global fields [See also 14G25] 


11G40 
$L$functions of varieties over global fields; BirchSwinnertonDyer conjecture [See also 14G10] 


11G42 
Arithmetic mirror symmetry [See also 14J33] 


11G45 
Geometric class field theory [See also 11R37, 14C35, 19F05] 


11G50 
Heights [See also 14G40, 37P30] 


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 nonArchimedean 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 


11J87 
Schmidt Subspace Theorem and applications 


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, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63] 


11K31 
Special sequences 


11K36 
Welldistributed sequences and other variations 


11K38 
Irregularities of distribution, discrepancy [See also 11Nxx] 


11K41 
Continuous, $p$adic and abstract analogues 


11K45 
Pseudorandom 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 


11M32 
Multiple Dirichlet series and zeta functions and multizeta values 


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 algebrogeometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72} 


11M45 
Tauberian theorems [See also 40E05] 


11M50 
Relations with random matrices 


11M55 
Relations with noncommutative geometry 


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 
Goldbachtype theorems; other additive questions involving primes 


11P55 
Applications of the HardyLittlewood method [See also 11D85] 


11P70 
Inverse problems of additive number theory, including sumsets 


11P81 
Elementary theory of partitions [See also 05A17] 


11P82 
Analytic theory of partitions 


11P83 
Partitions; congruences and congruential restrictions 


11P84 
Partition identities; identities of RogersRamanujan type 


11P99 
None of the above, but in this section 


11R04 
Algebraic numbers; rings of algebraic integers 


11R06 
PVnumbers and generalizations; other special algebraic numbers; Mahler measure 


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, 19A31] 


11R37 
Class field theory 


11R39 
LanglandsWeil 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, 16Hxx, 16Kxx] 


11R56 
Adèle rings and groups 


11R58 
Arithmetic theory of algebraic function fields [See also 14XX] 


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 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 
LanglandsWeil 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] 


11S70 
$K$theory of local fields [See also 19Fxx] 


11S80 
Other analytic theory (analogues of beta and gamma functions, $p$adic integration, etc.) 


11S82 
NonArchimedean dynamical systems [See mainly 37Pxx] 


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 halfplanes 


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 


11Z99 
None of the above, but in this section 