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.
|
11Axx
|
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
|
11Bxx
|
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 1k,2k,
|
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
|
11Cxx
|
Polynomials and matrices
|
11C08
|
Polynomials
[See also
13F20]
|
11C20
|
Matrices, determinants
[See also
15A36]
|
11C99
|
None of the above, but in this section
|
11Dxx
|
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
|
11Exx
|
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
|
11Fxx
|
Discontinuous groups and automorphic forms
[See also
11R39,
11S37,
14-XX,
22Exx,
14Gxx,
14Kxx,
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
|
11Gxx
|
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
|
Drinfel'd modules; higher-dimensional motives, etc.
[See also
14L05]
|
11G10
|
Abelian varieties of dimension \gtr
[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 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
|
11G55
|
Polylogarithms and relations with K-theory
|
11G99
|
None of the above, but in this section
|
11Hxx
|
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
|
11Jxx
|
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
|
11Kxx
|
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
|
11Lxx
|
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
|
11Mxx
|
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
|
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
|
11Nxx
|
Multiplicative number theory
|
11N05
|
Distribution of primes
|
11N13
|
Primes in progressions
[See also
11B25]
|
11N25
|
Distribution of integers with specified multiplicative constraints
|
11N30
|
Tur\'an 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
|
11Pxx
|
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
|
11Rxx
|
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
|
Adele 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
|
11Sxx
|
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
|
11Txx
|
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
|
11Uxx
|
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
|
11Yxx
|
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
|