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Navegando por la clasificación temática MSC 2000: 11 · Number theory
11 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
  11-04 Explicit machine computation and programs (not the theory of computation or programming)
  11-06 Proceedings, conferences, collections, etc.
  11-99 Number theory (not classified at a more specific level)
  11A Elementary number theory {For analogues in number fields, see 11R04}
    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
  11B Sequences and sets
    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
  11C Polynomials and matrices
    11C08 Polynomials [See also 13F20]
    11C20 Matrices, determinants [See also 15A36]
    11C99 None of the above, but in this section
  11D Diophantine equations [See also 11Gxx, 14Gxx]
    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
  11E Forms and linear algebraic groups [See also 19Gxx] {For quadratic forms in linear algebra, see 15A63}
    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
  11F Discontinuous groups and automorphic forms [See also 11R39, 11S37, 14-XX, 14Gxx, 14Kxx, 22Exx, 22E50, 22E55, 30F35, 32Nxx] {For relations with quadratic forms, see 11E45}
    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 Drinfel'd 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
  11G Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14-XX, 14Gxx, 14Kxx]
    11G05 Elliptic curves over global fields [See also 14H52]
    11G07 Elliptic curves over local fields [See also 14G20, 14H52]
    11G09 Drinfeld 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
  11H Geometry of numbers {For applications in coding theory, see 94B75}
    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
  11J Diophantine approximation, transcendental number theory [See also 11K60]
    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; Gelfond'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 Drinfel'd 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
  11K Probabilistic theory: distribution modulo $1$; metric theory of algorithms
    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
  11L Exponential sums and character sums {For finite fields, see 11Txx}
    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
  11M Zeta and $L$-functions: analytic theory
    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
  11N Multiplicative number theory
    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
  11P Additive number theory; partitions
    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
  11R Algebraic number theory: global fields {For complex multiplication, see 11G15}
    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
  11S Algebraic number theory: local and $p$-adic fields
    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
  11T Finite fields and commutative rings (number-theoretic aspects)
    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
  11U Connections with logic
    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
  11Y Computational number theory [See also 11-04]
    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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