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Biblioteca Dr. Antonio Monteiro · Catálogo |
| 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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