数学分支11部分数论英文1

Mathematics Subject Classification – MSC2020

11-XXNumber theory 

  178553

11-00General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to number theory 

  62

11-01Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory 

  1944

11-02Research exposition (monographs, survey articles) pertaining to number theory 

  2533

11-03History of number theory [Consider also classification numbers from Section 01-XX] 

  2091

11-04Software, source code, etc. for problems pertaining to number theory 

  1068

11-06Proceedings, conferences, collections, etc. pertaining to number theory 

  1498

11-11Research data for problems pertaining to number theory 

  3

11AxxElementary number theory {For analogues in number fields, see 11R04} 

  21123

11A05Multiplicative structure; Euclidean algorithm; greatest common divisors 

  1516

11A07Congruences; primitive roots; residue systems 

  4068

11A15Power residues, reciprocity 

  1375

11A25Arithmetic functions; related numbers; inversion formulas 

  5112

11A41Primes 

  2746

11A51Factorization; primality 

  1344

11A55Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15] 

  2846

11A63Radix representation; digital problems {For metric results, see 11K16} 

  2854

11A67Other number representations 

  635

11A99None of the above, but in this section 

  696

11BxxSequences and sets 

  31871

11B05Density, gaps, topology 

  1170

11B13Additive bases, including sumsets [See also 05B10] 

  1736

11B25Arithmetic progressions [See also 11N13] 

  1566

11B30Arithmetic combinatorics; higher degree uniformity 

  1217

11B34Representation functions 

  449

11B37Recurrences {For applications to special functions, see 33-XX} 

  4086

11B39Fibonacci and Lucas numbers and polynomials and generalizations 

  8125

11B50Sequences (mod mm) 

  1175

11B57Farey sequences; the sequences 1k,2k,…1k,2k,… 

  443

11B65Binomial coefficients; factorials; qq-identities [See also 05A10, 05A30] 

  3529

11B68Bernoulli and Euler numbers and polynomials 

  4447

11B73Bell and Stirling numbers 

  1955

11B75Other combinatorial number theory 

  3248

11B83Special sequences and polynomials 

  4976

11B85Automata sequences 

  1023

11B99None of the above, but in this section 

  453

11CxxPolynomials and matrices 

  3960

11C08Polynomials in number theory [See also 13F20] 

  2295

11C20Matrices, determinants in number theory [See also 15B36] 

  1636

11C99None of the above, but in this section 

  61

11DxxDiophantine equations [See also 11Gxx, 14Gxx] 

  14746

11D04Linear Diophantine equations 

  1201

11D07The Frobenius problem 

  339

11D09Quadratic and bilinear Diophantine equations 

  2602

11D25Cubic and quartic Diophantine equations 

  2347

11D41Higher degree equations; Fermat’s equation 

  2655

11D45Counting solutions of Diophantine equations 

  1269

11D57Multiplicative and norm form equations 

  505

11D59Thue-Mahler equations 

  282

11D61Exponential Diophantine equations 

  2080

11D68Rational numbers as sums of fractions 

  277

11D72Diophantine equations in many variables [See also 11P55] 

  1114

11D75Diophantine inequalities [See also 11J25] 

  735

11D79Congruences in many variables 

  465

11D85Representation problems [See also 11P55] 

  984

11D88pp-adic and power series fields 

  325

11D99None of the above, but in this section 

  553

11ExxForms and linear algebraic groups [See also 19Gxx] {For quadratic forms in linear algebra, see 15A63} 

  10137

11E04Quadratic forms over general fields 

  1159

11E08Quadratic forms over local rings and fields 

  410

11E10Forms over real fields 

  319

11E12Quadratic forms over global rings and fields 

  1310

11E16General binary quadratic forms 

  1671

11E20General ternary and quaternary quadratic forms; forms of more than two variables 

  902

11E25Sums of squares and representations by other particular quadratic forms 

  1801

11E39Bilinear and Hermitian forms 

  535

11E41Class numbers of quadratic and Hermitian forms 

  543

11E45Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) 

  891

11E57Classical groups [See also 14Lxx, 20Gxx] 

  536

11E70KK-theory of quadratic and Hermitian forms 

  110

11E72Galois cohomology of linear algebraic groups [See also 20G10] 

  439

11E76Forms of degree higher than two 

  814

11E81Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24] 

  1058

11E88Quadratic spaces; Clifford algebras [See also 15A63, 15A66] 

  396

11E95pp-adic theory 

  306

11E99None of the above, but in this section 

  111

11FxxDiscontinuous groups and automorphic forms [See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] {For relations with quadratic forms, see 11E45} 

  23591

11F03Modular and automorphic functions 

  1756

11F06Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40] 

  1177

11F11Holomorphic modular forms of integral weight 

  3528

11F12Automorphic forms, one variable 

  980

11F20Dedekind eta function, Dedekind sums 

  1231

11F22Relationship to Lie algebras and finite simple groups 

  501

11F23Relations with algebraic geometry and topology 

  226

11F25Hecke-Petersson operators, differential operators (one variable) 

  691

11F27Theta series; Weil representation; theta correspondences 

  2993

11F30Fourier coefficients of automorphic forms 

  2153

11F32Modular correspondences, etc. 

  257

11F33Congruences for modular and pp-adic modular forms 

  1529

11F37Forms of half-integer weight; nonholomorphic modular forms 

  1549

11F41Automorphic forms on GL(2)GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14G35] 

  1144

11F46Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms 

  1563

11F50Jacobi forms 

  686

11F52Modular forms associated to Drinfel’d modules 

  212

11F55Other groups and their modular and automorphic forms (several variables) 

  1077

11F60Hecke-Petersson operators, differential operators (several variables) 

  361

11F66Langlands LL-functions; one variable Dirichlet series and functional equations 

  1895

11F67Special values of automorphic LL-series, periods of automorphic forms, cohomology, modular symbols 

  2486

11F68Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series 

  99

11F70Representation-theoretic methods; automorphic representations over local and global fields 

  3741

11F72Spectral theory; trace formulas (e.g., that of Selberg) 

  1829

11F75Cohomology of arithmetic groups 

  723

11F77Automorphic forms and their relations with perfectoid spaces [See also 14G45] 

  29

11F80Galois representations 

  2249

11F85pp-adic theory, local fields [See also 14G20, 22E50] 

  1011

11F99None of the above, but in this section 

  213

11GxxArithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14Gxx, 14Kxx] 

  16088

11G05Elliptic curves over global fields [See also 14H52] 

  4476

11G07Elliptic curves over local fields [See also 14G20, 14H52] 

  559

11G09Drinfel’d modules; higher-dimensional motives, etc. [See also 14L05] 

  1005

11G10Abelian varieties of dimension >1>1 [See also 14Kxx] 

  1604

11G15Complex multiplication and moduli of abelian varieties [See also 14K22] 

  1147

11G16Elliptic and modular units [See also 11R27] 

  239

11G18Arithmetic aspects of modular and Shimura varieties [See also 14G35] 

  2062

11G20Curves over finite and local fields [See also 14H25] 

  2109

11G25Varieties over finite and local fields [See also 14G15, 14G20] 

  986

11G30Curves of arbitrary genus or genus ≠1≠1 over global fields [See also 14H25] 

  1033

11G32Arithmetic aspects of dessins d’enfants, Belyĭ theory 

  140

11G35Varieties over global fields [See also 14G25] 

  1098

11G40LL-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10] 

  1592

11G42Arithmetic mirror symmetry [See also 14J33] 

  35

11G45Geometric class field theory [See also 11R37, 14C35, 19F05] 

  143

11G50Heights [See also 14G40, 37P30] 

  1271

11G55Polylogarithms and relations with KK-theory 

  495

11G99None of the above, but in this section 

  198

11HxxGeometry of numbers {For applications in coding theory, see 94B75} 

  4527

11H06Lattices and convex bodies (number-theoretic aspects) [See also 11P21, 52C05, 52C07] 

  2057

11H16Nonconvex bodies 

  133

11H31Lattice packing and covering (number-theoretic aspects) [See also 05B40, 52C15, 52C17] 

  812

11H46Products of linear forms 

  203

11H50Minima of forms 

  465

11H55Quadratic forms (reduction theory, extreme forms, etc.) 

  810

11H56Automorphism groups of lattices 

  215

11H60Mean value and transfer theorems 

  121

11H71Relations with coding theory 

  242

11H99None of the above, but in this section 

  250

11JxxDiophantine approximation, transcendental number theory [See also 11K60] 

  11617

11J04Homogeneous approximation to one number 

  542

11J06Markov and Lagrange spectra and generalizations 

  263

11J13Simultaneous homogeneous approximation, linear forms 

  824

11J17Approximation by numbers from a fixed field 

  232

11J20Inhomogeneous linear forms 

  211

11J25Diophantine inequalities [See also 11D75] 

  588

11J54Small fractional parts of polynomials and generalizations 

  215

11J61Approximation in non-Archimedean valuations 

  614

11J68Approximation to algebraic numbers 

  710

11J70Continued fractions and generalizations [See also 11A55, 11K50] 

  2116

11J71Distribution modulo one [See also 11K06] 

  1046

11J72Irrationality; linear independence over a field 

  864

11J81Transcendence (general theory) 

  1865

11J82Measures of irrationality and of transcendence 

  772

11J83Metric theory 

  948

11J85Algebraic independence; Gel’fond’s method 

  734

11J86Linear forms in logarithms; Baker’s method 

  1060

11J87Schmidt Subspace Theorem and applications 

  171

11J89Transcendence theory of elliptic and abelian functions 

  199

11J91Transcendence theory of other special functions 

  698

11J93Transcendence theory of Drinfel’d and tt-modules 

  104

11J95Results involving abelian varieties 

  97

11J97Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.) 

  174

11J99None of the above, but in this section 

  371

11KxxProbabilistic theory: distribution modulo 11; metric theory of algorithms 

  9685

11K06General theory of distribution modulo 11 [See also 11J71] 

  1644

11K16Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63] 

  1107

11K31Special sequences 

  583

11K36Well-distributed sequences and other variations 

  375

11K38Irregularities of distribution, discrepancy [See also 11Nxx] 

  1533

11K41Continuous, pp-adic and abstract analogues 

  144

11K45Pseudo-random numbers; Monte Carlo methods [See also 65C05, 65C10] 

  1292

11K50Metric theory of continued fractions [See also 11A55, 11J70] 

  759

11K55Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx] 

  1347

11K60Diophantine approximation in probabilistic number theory [See also 11Jxx] 

  828

11K65Arithmetic functions in probabilistic number theory [See also 11Nxx] 

  1345

11K70Harmonic analysis and almost periodicity in probabilistic number theory 

  171

11K99None of the above, but in this section 

  394

11LxxExponential sums and character sums {For finite fields, see 11Txx} 

  6147

11L03Trigonometric and exponential sums (general theory) 

  1556

11L05Gauss and Kloosterman sums; generalizations 

  1602

11L07Estimates on exponential sums 

  1701

11L10Jacobsthal and Brewer sums; other complete character sums 

  189

11L15Weyl sums 

  266

11L20Sums over primes 

  374

11L26Sums over arbitrary intervals 

  51

11L40Estimates on character sums 

  1225

11L99None of the above, but in this section 

  114

11MxxZeta and LL-functions: analytic theory 

  13908

11M06ζ(s)ζ(s) and L(s,χ)L(s,χ) 

  5543

11M20Real zeros of L(s,χ)L(s,χ); results on L(1,χ)L(1,χ) 

  397

11M26Nonreal zeros of ζ(s)ζ(s) and L(s,χ)L(s,χ); Riemann and other hypotheses 

  2053

11M32Multiple Dirichlet series and zeta functions and multizeta values 

  1224

11M35Hurwitz and Lerch zeta functions 

  1715

11M36Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) 

  1067

11M38Zeta and LL-functions in characteristic pp 

  511

11M41Other 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] 

  3449

11M45Tauberian theorems [See also 40E05] 

  162

11M50Relations with random matrices 

  326

11M55Relations with noncommutative geometry 

  83

11M99None of the above, but in this section 

  292

11NxxMultiplicative number theory 

  13483

11N05Distribution of primes 

  2827

11N13Primes in congruence classes 

  1159

11N25Distribution of integers with specified multiplicative constraints 

  1658

11N30Turán theory [See also 30Bxx] 

  90

11N32Primes represented by polynomials; other multiplicative structures of polynomial values 

  446

11N35Sieves 

  1028

11N36Applications of sieve methods 

  1435

11N37Asymptotic results on arithmetic functions 

  5081

11N45Asymptotic results on counting functions for algebraic and topological structures 

  725

11N56Rate of growth of arithmetic functions 

  574

11N60Distribution functions associated with additive and positive multiplicative functions 

  592

11N64Other results on the distribution of values or the characterization of arithmetic functions 

  777

11N69Distribution of integers in special residue classes 

  477

11N75Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx] 

  109

11N80Generalized primes and integers 

  362

11N99None of the above, but in this section 

  164

11PxxAdditive number theory; partitions 

  11199

11P05Waring’s problem and variants 

  1727

11P21Lattice points in specified regions 

  1325

11P32Goldbach-type theorems; other additive questions involving primes 

  1925

11P55Applications of the Hardy-Littlewood method [See also 11D85] 

  1491

11P70Inverse problems of additive number theory, including sumsets 

  612

11P81Elementary theory of partitions [See also 05A17] 

  2630

11P82Analytic theory of partitions 

  880

11P83Partitions; congruences and congruential restrictions 

  1635

11P84Partition identities; identities of Rogers-Ramanujan type 

  698

11P99None of the above, but in this section 

  479

11RxxAlgebraic number theory: global fields {For complex multiplication, see 11G15} 

  24065

11R04Algebraic numbers; rings of algebraic integers