Markov processes on the adeles and Chebyshev function
Keywords: عملکرد ریمان زتا; Markov processes; Adeles; Riemann zeta function
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Self-intersections of the Riemann zeta function on the critical line
Keywords: عملکرد ریمان زتا; Self-intersections; Riemann zeta function; Critical line
A multidimensional half-discrete Hilbert-type inequality and the Riemann zeta function
Keywords: عملکرد ریمان زتا; Gamma function; Riemann zeta function; Numerical estimates; Half-discrete Hilbert’s inequality; Weight function; Hermite–Hadamard’s inequality; Hilbert’s operator; Equivalent form
New definite integrals and a two-term dilogarithm identity
Keywords: عملکرد ریمان زتا; Euler sums; Riemann zeta function; Double integrals; Hyperbolic functions; Dilogarithm identities
On some expansions for the Euler Gamma function and the Riemann Zeta function
Keywords: عملکرد ریمان زتا; 11B83; 11M06; Euler Gamma function; Riemann Zeta function; Bell polynomials; Potential polynomials; Mittag-Leffler polynomials; Derivative polynomials;
Explicit relations between pair correlation of zeros and primes in short intervals
Keywords: عملکرد ریمان زتا; Primes in short intervals; Riemann zeta function; Pair correlation of zeros
Riemann zeta function and Lyapunov-type inequalities for certain higher order differential equations
Keywords: عملکرد ریمان زتا; Lyapunov inequality; Sobolev inequality; Best constant; Riemann zeta function
The action of Hecke operators to families of Weierstrass-type functions and Weber-type functions and their applications
Keywords: عملکرد ریمان زتا; Generalized Dedekind eta functions; Eisenstein series; Theta functions; Hecke operators; Weierstrass type functions; Weber functions; Bernoulli numbers; Riemann zeta function
Inequalities associated with Barnes G-function
Keywords: عملکرد ریمان زتا; 33B15; 26A48; Gamma function; Psi function; Polygamma functions; Barnes G-function; Inequality; Riemann zeta function;
Asymptotic formulas for the triple Gamma function Î3 by means of its integral representation
Keywords: عملکرد ریمان زتا; Gamma, double, triple and multiple Gamma functions; Riemann Zeta function; Hurwitz (or generalized) Zeta function; Psi (or Digamma) function; Bernoulli numbers; Bohr-Mollerup theorem; Euler-Mascheroni and Glaisher-Kinkelin constant; Determinants of the La
Some summation formulas involving harmonic numbers and generalized harmonic numbers
Keywords: عملکرد ریمان زتا; Harmonic numbers; Generalized harmonic numbers; Riemann Zeta function; Hurwitz Zeta function; Stirling numbers of the first kind; Generalized hypergeometric function pFqpFq; Summation formulas for pFqpFq; Psi function; Polygamma functions
Mathieu series and associated sums involving the Zeta functions
Keywords: عملکرد ریمان زتا; Euler–Mascheroni constant; Gamma function; Psi (or Digamma) function; Trigamma and Polygamma functions; Riemann Zeta function; Hurwitz (or generalized) Zeta function; Dirichlet Eta function; Bernoulli numbers; Mathieu series; Alternating Mathieu series; F
Exponential and trigonometric sums associated with the Lerch zeta and Legendre chi functions
Keywords: عملکرد ریمان زتا; Trigonometric and exponential sums; Hurwitz zeta function; Lerch zeta function; Riemann zeta function; Legendre chi function; Discrete Fourier transform; Bernoulli polynomials and numbers; Eisenstein summation formula; Wang sums; Williams–Zhang sums
A main inequality for several special functions
Keywords: عملکرد ریمان زتا; A generalization of Cauchy–Bunyakovsky–Schwarz inequality; Classical special functions; Laplace and Fourier integral transforms; Elliptic integrals; Riemann zeta function
On the occurrence of the sine kernel in connection with the shifted moments of the Riemann zeta function
Keywords: عملکرد ریمان زتا; Riemann zeta function; Mean value theorem; Correlation; Sine kernel; Random matrix theory;
On a generalization of Chen's iterated integrals
Keywords: عملکرد ریمان زتا; primary, 11G55; secondary, 11M99, 33E20Iterated integrals; Monodromy of polylogarithms; Dedekind zeta function; Riemann zeta function; Homotopy functionals; Multi-zeta functions; Iterated derivatives
Some discrete Fourier transform pairs associated with the Lipschitz–Lerch Zeta function
Keywords: عملکرد ریمان زتا; Hurwitz–Lerch Zeta function; Lipschitz–Lerch Zeta function; Lerch Zeta function; Hurwitz Zeta function; Riemann Zeta function; Legendre chi function; Bernoulli polynomials; Bernoulli numbers; Discrete Fourier transform
Some results involving series representations of hypergeometric functions
Keywords: عملکرد ریمان زتا; 33C20; 33C05; 33B10Hypergeometric functions; Riemann zeta function; Beta function; Series representation
Summation properties of the ηjηj and Li constants
Keywords: عملکرد ریمان زتا; Binomial transform; Li constants; Riemann zeta function; Riemann xi function; Logarithmic derivatives; Riemann hypothesis; Li criterion; Laurent expansion
An efficient algorithm for the Hurwitz zeta and related functions
Keywords: عملکرد ریمان زتا; 11M06; 11M35; 33B15; Hurwitz zeta function; Riemann zeta function; Polygamma function; Lerch zeta function; Algorithm; Integral representation; Generalized harmonic numbers; Stieltjes constants;
On some series representations of the Hurwitz zeta function
Keywords: عملکرد ریمان زتا; 11M06; 11M35; 33B15; Hurwitz zeta function; Riemann zeta function; Polygamma function; Lerch zeta function; Series representation; Integral representation; Generalized harmonic numbers;
Distributions and moments of record values in a sequence of maximally dependent random variables
Keywords: عملکرد ریمان زتا; primary 60E15; secondary 60G70; 05A30; Maximally dependent sequence; Exchangeable sequence; Sample maximum; Record time; Record value; Stochastic order; Signless Stirling numbers of first kind; Riemann zeta function;
Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n, and the multiple Hurwitz zeta function
Keywords: عملکرد ریمان زتا; Gamma function; Multiple Gamma functions; Riemann Zeta function; Hurwitz Zeta function; Hurwitz-Lerch Zeta function; Multiple Hurwitz-Lerch Zeta function; q-Extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials and numbers of highe
On the Hurwitz function for rational arguments
Keywords: عملکرد ریمان زتا; Riemann zeta function; Hurwitz zeta function; Multiple gamma function; Stirling numbers; Bernoulli numbers; Euler numbers; Glaisher’s numbers; Derivatives of the cotangent
Some families of Mathieu a-series and alternating Mathieu a-series
Keywords: عملکرد ریمان زتا; Mathieu and alternating Mathieu series; Mathieu and alternating Mathieu a-series; Mellin transforms; Asymptotic expansions; Bernoulli numbers; Bessel function of the first kind; Dirichlet Eta function; Dirichlet series; Euler-Maclaurin summation formula
Remark on a double-inequality for the Riemann zeta function
Keywords: عملکرد ریمان زتا; primary 11M06; secondary 26D15; Riemann zeta function; Inequalities;
Certain families of series associated with the Hurwitz-Lerch Zeta function
Keywords: عملکرد ریمان زتا; Multiple Gamma functions; Riemann Zeta function; Generalized (or Hurwitz) Zeta function; Hurwitz-Lerch Zeta function; Psi (or Digamma) function; Determinants of Laplacians; Harmonic numbers; Series identities; Summation formulas;
On some integrals involving functions Ï(x) such that Ï(1/x)=xÏ(x)
Keywords: عملکرد ریمان زتا; Riemann zeta function; Integrals involving theta function; Integral equations; Bessel functions;
On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams
Keywords: عملکرد ریمان زتا; 33B; 33E; 11M; Gamma function; Digamma function; Polygamma function; Riemann zeta function; Clausen function; Euler sums; Harmonic numbers; Hurwitz zeta function; Hypergeometric function; Dilogarithm function; Trilogarithm function; Polylogarithm function