Keywords: primary; 11B65; secondary; 05A10; Binomial coefficients; p-adic valuation; Lucas' theorem; Euler's totient theorem; Bernoulli numbers;
مقالات ISI (ترجمه نشده)
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Keywords: primary; 05A10; 05A19; 33C20; secondary; 11B65; 11B83; 11M06; Polygamma function; Integral representation; Logarithmic integral; Riemann zeta function;
Keywords: 15B05; 11B39; 11B65; Dual sequence; Dual matrix; Vandermonde matrix; Hankel matrix; Toeplitz matrix; Lagrange interpolation polynomial;
Keywords: primary; 11B65; 05A16; secondary; 11A63; 11B50; Binomial coefficients; Central limit law; Divisibility by powers of primes; Multivariate asymptotics of generating functions;
Keywords: primary; 11B65; secondary; 05A10; Binomial coefficient; Catalan triangle; Chu-Vandermonde convolution; Telescoping method; Partial binomial sum;
Keywords: 11B65; 11A07; Supercongruences; Abelian squares;
Keywords: 15B18; 11B39; 11B65; Invariant sequence; Pascal matrix; Eigenvalue; Eigenvector;
Keywords: 11A07; 11B65; 05A10Congruence; Binomial coefficients; Gaussian binomial coefficients; q-Series; Cyclotomic polynomials
Keywords: 11A25; 11N32; 11N37; 11B65; 11A63Catalan numbers; Euler's function; Totient; Dickson's conjecture
Keywords: 11B65; 31B15; 13F20Integer valued polynomials; p-ordering; Valuative capacity; Transfinite diameter
Keywords: primary; 11A05; 11A07; secondary; 05A10; 11B65; Binomial coefficients; Divisibility; WZ method;
Keywords: primary; 11J70; secondary; 11B65; 11F11; 33E05; Kronecker limit formula; P-Q modular equation; Ramanujan-Weber class invariant; Reciprocity formula; Rogers-Ramanujan continued fraction;
Keywords: 11B65; 11F27q-Series; Hecke-type triple-sums; Appell–Lerch functions
Keywords: 05A15; 05A19; 05A30; 11B65; 11B73; 11B83Rook numbers; q-Analogues; Elliptic extensions; Alpha-parameter model; Matchings
On the equation A!B! = C!
Keywords: 11B65; 11D85; 11B05; Products of factorials; Primes in intervals;
On the DLW conjectures
Keywords: 05C35; 11T06; 11B65; Finite field; Monomial graph; Permutation polynomial;
The Frobenius number for sequences of triangular and tetrahedral numbers
Keywords: 11D07; 11B65; Frobenius number; Triangular numbers; Tetrahedral numbers; Telescopic sequences; Free numerical semigroups;
Arithmetic properties of Delannoy numbers and Schröder numbers
Keywords: primary; 11A07; 11B75; secondary; 05A10; 05A19; 11B65; 11C08; 33F99; Congruence; Polynomial; Delannoy number; Schröder number; Motzkin number;
Proof of two conjectural supercongruences involving Catalan-Larcombe-French numbers
Keywords: primary; 11B65; 11B68; secondary; 05A10; 11A07; Central binomial coefficients; Supercongruence; Harmonic numbers;
The Rodriguez-Villegas type congruences for truncated q-hypergeometric functions
Keywords: primary; 11B65; secondary; 05A10; 05A30; Congruences; Truncated q-hypergeometric function; Cyclotomic polynomial; q-Chu-Vandermonde identity;
The 2-adic valuation of generalized Fibonacci sequences with an application to certain Diophantine equations
Keywords: 11B39; 11B65; 11D99; Generalized Fibonacci sequences; Diophantine equations; Factorials; p-adic valuation;
(Ï,q)-Volkenborn integration
Keywords: 05A30; 11B65; 11B68; 11S23; q-Volkenborn integral; Carlitz's q-Bernoulli polynomials; (Ï,q)-calculus; p-adic number;
Homogeneous q-partial difference equations and some applications
Keywords: 05A30; 11B65; 33D15; 33D45; 39A13; Homogeneous q-partial difference equation; Generating function; q-hypergeometric polynomial; Askey-Roy integral; Andrews-Askey integral; Ramanujan's integral; Moment integral;
Continued fractions and q-series generating functions for the generalized sum-of-divisors functions
Keywords: 11J70; 11Y65; 40A30; 11B65; 11A25; Divisor function; Sum of divisors function; Continued fraction; J-fraction;
Supercongruences involving dual sequences
Keywords: primary; 11A07; 11B65; secondary; 05A10; 05A19; 11B68; 11B75; p-adic congruences; Binomial coefficients; Combinatorial identities; Dual sequences;
A supercongruence involving Delannoy numbers and Schröder numbers
Keywords: 11A07; 11B65; 11B83; 05A10Supercongruence; Delannoy numbers; Schröder numbers; Bernoulli numbers
Inverse of some matrix related to double zeta values of odd weight
Keywords: 11B65; 11B68; 11M32Double zeta value of odd weight; Bernoulli number identity
On the families of q-Euler polynomials and their applications
Keywords: 05A10; 11B65; 11B68; 11B73Euler numbers and polynomials; q-Euler numbers and polynomials; Weighted q-Euler numbers and polynomials; Weighted q-Euler-Zeta function; p-adic q -integral on ZpZp
Proof of a conjecture of Z.-W. Sun on the divisibility of a triple sum
Keywords: 11A07; 11B65; 05A10Congruence; Supercongruence; Zeilberger's algorithm
Finite and infinite Rogers–Ramanujan continued fractions in Ramanujan's lost notebook
Keywords: 11B65; 11A55Rogers–Ramanujan continued fraction; Finite Rogers–Ramanujan continued fraction; Explicit values
Supercongruences motivated by e
Keywords: primary; 11B65; secondary; 05A10; 11A07; 11B68; Supercongruences; Binomial coefficients; Bernoulli numbers;
On the Gauss E ϒPHKA theorem and some allied inequalities
Keywords: 11B65; 11E12; 11E16; 11E20; 11E25; 11E41; 11F37θ-Function identities; Representation properties; Spinor regular ternary quadratic forms; 1907 Hurwitz formula
Hankel determinant calculus for the Thue-Morse and related sequences
Keywords: 05A10; 05A15; 11B50; 11B65; 11B85; 11C20; 11J82; 11Y65; 15A15; 30B70; Hankel determinant; Continued fraction; Automatic sequence; Thue-Morse sequence; Stieltjes algorithm; Grafting technique; Chopping method;
On divisibility of sums of Apéry polynomials
Keywords: primary; 11A07; secondary; 11B65; 11B83; 05A10; Apéry polynomial; q-Lucas congruence;
On the dual nature of partial theta functions and Appell–Lerch sums
Keywords: 11B65; 11F11; 11F27Hecke-type double sums; Appell–Lerch sums; Mock theta functions; Indefinite theta series; Partial theta functions
Binary quadratic forms and the Fourier coefficients of certain weight 1 eta-quotients
Keywords: 11B65; 11F03; 11F11; 11F20; 11F27; 11E16; 11E20; 11E25; 14K25Eta-quotients; Binary quadratic forms; Theta series; Multiplicative functions; Hecke operators; Dissections of q-series
Connections between p=x2+3y2 and Franel numbers
Keywords: primary; 11A07; 11E25; secondary; 05A10; 11B65; 11B75; Primes of the form x2+3y2; Franel numbers; Congruences;
Some q-congruences related to 3-adic valuations
Keywords: primary; 11B65; secondary; 05A10; 05A30; 11A07; 11S99; 3-adic valuation; Central binomial coefficient; Congruence; q-analogue;
Congruences arising from Apéry-type series for zeta values
Keywords: 11B65; 05A10; 11B68; 11A07; 33F10; 11B39; 11M06; Congruence; Creative telescoping; WZ pair; Finite central binomial sum; Multiple harmonic sum; Bernoulli number; Apéry-like series; Zeta value;
Some congruences involving central q-binomial coefficients
Keywords: 11B65; 11A07; 05A10Central binomial coefficients; q-Binomial coefficient; Congruence; Cyclotomic polynomial
Newtonian and Schinzel sequences in a domain
Keywords: 13F20; 11B65; 13G05
Lattice paths and nn-colour compositions
Keywords: primary, 05A10; 05A15; 05A17; 05A19; secondary, 11B39; 11B65; 11P21; 11P81Compositions; nn-Colour compositions; Lattice paths; Binomial identites
Prime divisors of binary holonomic sequences
Keywords: 11A07; 11B65; 11L40Holonomic sequences; Prime numbers; Smooth numbers; The subspace theorem
Congruences for sums of binomial coefficients
Keywords: 11B65; 05A10; 11A07
A number-theoretic approach to homotopy exponents of SU(n)
Keywords: 55Q52; 57T20; 11A07; 11B65; 11S05;
Arithmetical properties of wendt's determinant
Keywords: 11C20; 11B65; 11A07; 11R18; Wendt's determinant; Binomial coefficients; Resultants; Cyclotomic fields;
Algebras of operations in K-theory
Keywords: primary: 55S25; secondary: 19L64; 11B65; K-theory operations; Gaussian polynomials;
On the properties of Newton-Euler pairs
Keywords: 11B83; 15A15; 11B68; 05A17; 11A25; 11B73; 11B65; 11B39; Newton-Euler pair; Newton-Euler sequence; The sum of divisors; The number of partitions; Bernoulli numbers;