| 11-XX | | Prev: 08 | Up: Top | Next: 12 | |
| 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)
[xref: 11Yxx]
| 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]
[xref: 11J70, 11K50, 30B70]
| 11A63 |
Radix representation; digital problems {For metric results, see 11K16}
[xref: 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]
[xref: 05B10]
| 11B25 |
Arithmetic progressions [See also 11N13]
[xref: 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]
[xref: 05A10]
| 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]
[xref: 13B25, 13F20]
| 11C20 |
Matrices, determinants [See also 15A36]
| 11C99 |
None of the above, but in this section
| |
11Dxx |
Diophantine equations [See also 11Gxx, 14Gxx]
[xref: 11Gxx, 14Gxx, 14H25, 14J20, 14K15]
| 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]
[xref: 11J25]
| 11D79 |
Congruences in many variables
| 11D85 |
Representation problems [See also 11P55]
[xref: 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}
[xref: 12D15, 18F25]
| 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]
[xref: 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}
[xref: 11N75, 11R39, 11S37, 14K15, 30F35, 32Nxx]
| 11F03 |
Modular and automorphic functions
| 11F06 |
Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40]
[xref: 20H05, 20H10]
| 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]
[xref: 14G35]
| 11F46 |
Siegel modular groups and their modular and automorphic forms
[xref: 14G35]
| 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]
[xref: 11Dxx, 14Gxx, 14K15]
| 11G05 |
Elliptic curves over global fields [See also 14H52]
[xref: 14H25, 14H52]
| 11G07 |
Elliptic curves over local fields [See also 14G20, 14H52]
[xref: 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]
[xref: 14K10, 14K22]
| 11G16 |
Elliptic and modular units [See also 11R27]
| 11G18 |
Arithmetic aspects of modular and Shimura varieties [See also 14G35]
[xref: 14G35]
| 11G20 |
Curves over finite and local fields [See also 14H25]
| 11G25 |
Varieties over finite and local fields [See also 14G15, 14G20]
[xref: 14J20]
| 11G30 |
Curves of arbitrary genus or genus $\ne 1$ over global fields [See also 14H25]
| 11G35 |
Varieties over global fields [See also 14G25]
[xref: 14J20]
| 11G40 |
$L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]
[xref: 14G10, 19F27]
| 11G45 |
Geometric class field theory [See also 11R37, 14C35, 19F05]
[xref: 19F05]
| 11G50 |
Heights [See also 14G40]
[xref: 14G40]
| 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}
[xref: 52C10]
| 11H06 |
Lattices and convex bodies [See also 11P21, 52C05, 52C07]
[xref: 52C05, 52C07]
| 11H16 |
Nonconvex bodies
| 11H31 |
Lattice packing and covering [See also 05B40, 52C15, 52C17]
[xref: 05B40, 52C05, 52C07, 52C15, 52C17, 94B75]
| 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]
[xref: 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]
[xref: 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]
[xref: 11K50]
| 11J71 |
Distribution modulo one [See also 11K06]
[xref: 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
[xref: 37A45]
| 11K06 |
General theory of distribution modulo $1$ [See also 11J71]
[xref: 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]
[xref: 11A55, 11J70, 28Dxx]
| 11K55 |
Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]
[xref: 28Dxx]
| 11K60 |
Diophantine approximation [See also 11Jxx]
[xref: 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}
[xref: 11R42, 11S40, 30B50]
| 11M45 |
Tauberian theorems [See also 40E05]
| 11M99 |
None of the above, but in this section
| |
11Nxx |
Multiplicative number theory
[xref: 11K38, 11K65, 11R47]
| 11N05 |
Distribution of primes
[xref: 11R44]
| 11N13 |
Primes in progressions [See also 11B25]
[xref: 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
[xref: 11K55]
| |
11Pxx |
Additive number theory; partitions
| 11P05 |
Waring's problem and variants
| 11P21 |
Lattice points in specified regions
[xref: 11H06, 52C05, 52C07]
| 11P32 |
Goldbach-type theorems; other additive questions involving primes
| 11P55 |
Applications of the Hardy-Littlewood method [See also 11D85]
[xref: 11D72, 11D85]
| 11P70 |
Inverse problems of additive number theory
| 11P81 |
Elementary theory of partitions [See also 05A17]
[xref: 05A17]
| 11P82 |
Analytic theory of partitions
[xref: 05A17]
| 11P83 |
Partitions; congruences and congruential restrictions
[xref: 05A17]
| 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
[xref: 11G16]
| 11R29 |
Class numbers, class groups, discriminants
[xref: 13C20]
| 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
[xref: 11G45, 19F15]
| 11R39 |
Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]
[xref: 11Fxx]
| 11R42 |
Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]
[xref: 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
[xref: 11S45, 12E15, 16H05]
| 11R54 |
Other algebras and orders, and their zeta and $L$-functions [See also 11S45, 16H05, 16Kxx]
[xref: 11S45, 12E15, 16H05]
| 11R56 |
Adele rings and groups
[xref: 43A70]
| 11R58 |
Arithmetic theory of algebraic function fields [See also 14-XX]
[xref: 14H05]
| 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]
[xref: 18F25]
| 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
[xref: 14E22]
| 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]
[xref: 11Fxx]
| 11S40 |
Zeta functions and $L$-functions [See also 11M41, 19F27]
[xref: 19F27]
| 11S45 |
Algebras and orders, and their zeta functions [See also 11R52, 11R54, 16H05, 16Kxx]
[xref: 11R54, 12E15, 16H05]
| 11S70 |
$K$-theory of local fields [See also 19Fxx]
[xref: 18F25]
| 11S80 |
Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.)
[xref: 12H25]
| 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
[xref: 94A60, 94B27, 94B40]
| 11T99 |
None of the above, but in this section
| |
11Uxx |
Connections with logic
| 11U05 |
Decidability [See also 03B25]
[xref: 03B25]
| 11U07 |
Ultraproducts [See also 03C20]
| 11U09 |
Model theory [See also 03Cxx]
| 11U10 |
Nonstandard arithmetic [See also 03H15]
[xref: 03H15]
| 11U99 |
None of the above, but in this section
| |
11Yxx |
Computational number theory [See also 11-04]
[xref: 68W30]
| 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
| |