Keywords: Trigonometric sums; Computational formula; Identity; Dirichlet L-functions; Bernoulli numbers; 11B68; 11M06;
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: primary; 11M06; Riemann zeta-function; Zeros; Simple zeros; Pair correlation;
Keywords: 40A25; 11B73; 11B83; 11M06; 05A15; Euler sums; Stirling sums; Bell polynomials; Generating functions; Riemann zeta function;
Keywords: 11B68; 11C20; 11M06; Bernoulli number; Bernoulli polynomial; Riemann zeta function; Euler number; Euler polynomial; Alternating zeta function; Double zeta values; Hurwitz zeta function; Lerch zeta function; Polygamma function; Ramanujan polynomial; Bernou
Keywords: primary; 11M06; secondary; 33E99; 33B15; Riemann zeta function; Odd integer; Raabe's integral; Abel's criteria; Bernoulli numbers;
Keywords: 11B37; 11B68; 11M06; 11M35; Bernoulli numbers and polynomials; Recurrence relations; Saalschütz-Gelfand's formula; Von Ettingshausen-Stern's formula; Riemann zeta-function; Dirichlet L-series;
Keywords: 11M06; 11M32; 33B99; 33E20; 40A05; Tornheim type series; Harmonic numbers; Polylogarithm function; Euler sums; Riemann zeta function;
Keywords: primary; 11M06; 33C10; secondary; 33E30; 11N37; Divisor problem; Circle problem; Ramanujan's Lost Notebook; Voronoï summation formula; Koshliakov transforms; Bessel functions; Self-reciprocal functions; Wigert's identity; Double Bessel series identities;
Keywords: 11M06; 11M32; 33B15Polylogarithm functions; Euler sums; Riemann zeta function
Keywords: 11M06; 11M26Riemann zeta-function; Alternative Hypothesis; Pair Correlation Conjecture
Keywords: Explicit formula; Derivative polynomial; Tangent number; Bernoulli number; Bell polynomial of the second kind; Euler polynomial11B68; 11B83; 33B10; 11C08; 11M06; 26A24,
Keywords: primary; 11M06; secondary; 33C10; Riemann Î-function; Bessel functions; Integral identities; Koshlyakov; Ramanujan;
Keywords: 11M06; 20C12; Bianchi groups; Module extensions;
Lehmer pairs and derivatives of Hardy's Z-function
Keywords: 11M06; 11M26; Lehmer pair; Hardy's Z-function; Riemann hypothesis;
Sum formulas of multiple zeta values with even arguments and polynomial weights
Keywords: primary; 40B05; secondary; 11M41; 11M06; 33E20; Multiple zeta values; Multiple zeta-star value; Weighted sum formula;
Mean values of derivatives of L-functions in function fields: II
Keywords: primary; 11M38; secondary; 11M06; 11G20; 11M50; 14G10; Function fields; Derivatives of L-functions; Moments of L-functions; Quadratic Dirichlet L-functions; Random matrix theory;
Continuous lower bounds for the moments of Dedekind zeta-functions
Keywords: 11M06; Dedekind zeta-function; Continuous lower bound;
Explicit bounds for L-functions on the edge of the critical strip
Keywords: primary; 11M06; 11M36; secondary; 11M41; L-functions; Explicit results;
Trilinear forms with Kloosterman fractions
Keywords: 11M06; 11M26; Kloosterman sums; Trilinear forms;
Zeros of the first derivative of Dirichlet L-functions
Keywords: 11M06; Dirichlet L-function; Derivative; Zeros;
On the distribution of positive and negative values of Hardy's Z-function
Keywords: 11M06; Riemann zeta-function; Hardy's function; Distribution of positive and negative values;
Decomposition theorems produced from differential operators
Keywords: primary; 40B05; secondary; 11M40; 11M06; 33E20; Multiple zeta value; Hurwitz zeta functions; Euler decomposition theorem;
Trigonometric series and special values of L-functions
Keywords: 11M06; 33B30; 33B10; Riemann zeta function; L-function; Generalized harmonic number; Legendre symbol; Clausen function; Best polynomial approximation;
Multiple zeta values and Euler sums
Keywords: 40B05; 33B15; 11M06; 11M41; Multiple zeta value; Multiple zeta star value; Multiple harmonic number; Multiple star harmonic number; Euler sum;
On a mollifier of the perturbed Riemann zeta-function
Keywords: primary; 11M36; secondary; 11M06; 11N64; Riemann zeta-function; Mollifier; Zeros on the critical line; Ratios conjecture technique; Generalized von Mangoldt function;
Algebraic differential equations with functional coefficients concerning ζ and Γ
Keywords: 34M15; 11M06; 33B15; 30D30Riemann zeta function; The Euler gamma function; Polynomial; Algebraic differential equation
On the zeros of Riemann's zeta-function on the critical line
Keywords: 11M06; 11M26Riemann zeta-function; Critical zeros; Mollified fourth moment
Analogues of Newton-Girard power-sum formulas for entire and meromorphic functions with applications to the Riemann zeta function
Keywords: primary; 30D20; 30D30; secondary; 11M06; 65Q30; Meromorphic functions; Entire functions; Functions of finite order; Zeros and poles; Sums of reciprocal powers of zeros and poles; Riemann zeta function; Nontrivial zeros of zeta function; Sums of powers of
Does the Riemann zeta function satisfy a differential equation?
Keywords: primary; 11M06; secondary; 34A35; Riemann zeta function; Infinite order differential equation; Euler-MacLauren summation formula;
On the mean values of Dirichlet L-functions
Keywords: 11M06; 11F20; 11B68; L-function; Character sum; Gauss sum; Bernoulli polynomial;
Integral representations of functions and Addison-type series for mathematical constants
Keywords: 11M06; 11Y60; 11M35Lerch zeta-function; Hurwitz zeta-function; Polylogarithm function; Dirichlet L-functions; Clausen functions; Generalized Somos constants; Glaisher–Kinkelin constant; Kinkelin constant; Stieltjes constants; Integral representation; Seri
Inverse binomial series and values of Arakawa–Kaneko zeta functions
Keywords: 11M06; 11M41; 11Y60; 33B30Harmonic sums; Binomial transformations; Bell polynomials; Polylogarithms; Log-sine integrals; Mellin transforms; Zeta values
Zeros of combinations of the Riemann ξ-function on bounded vertical shifts
Keywords: primary; 11M06; 11M26; Riemann zeta-function; Critical line; Zeros; Bounded vertical shifts; Ramanujan's Lost Notebook; Self-reciprocal functions; Theta transformation formula;
Zeros of the derivatives of the Riemann zeta function on Res<1/2
Keywords: 11M06; 11M26Riemann zeta function; Derivatives; Zero; Density hypothesis
Zeros and special values of Witten zeta functions and Witten L-functions
Keywords: 11M06; Witten zeta function; Witten L-function;
Non-vanishing of Dirichlet series with periodic coefficients
Keywords: 11M06; 11M20Okada's criterion; Non-vanishing of Dirichlet series; Linear forms in logarithms
On some expansions for the Euler Gamma function and the Riemann Zeta function
Keywords: 11B83; 11M06; Euler Gamma function; Riemann Zeta function; Bell polynomials; Potential polynomials; Mittag-Leffler polynomials; Derivative polynomials;
On joint universality of the Riemann zeta-function and Hurwitz zeta-functions
Keywords: 11M06; 11M41; Hurwitz zeta-function; Limit theorem; Mergelyan theorem; Riemann zeta-function; Space of analytic functions; Universality;
Deux extensions de Théorèmes de Hamburger (portant sur l’équation fonctionnelle de la fonction zêta)
Keywords: 11M06; 11F66Riemann zeta function; Dirichlet series; Hamburger theorem; Functional equations; co-Poisson formula; Poisson formula
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;
A uniqueness theorem for Dirichlet series satisfying a Riemann type functional equation
Keywords: 30D35; 11M06; 30D30; 11M41; L-function; Dirichlet series; Meromorphic function; Selberg class;
On the mean square average of special values of L-functions
Keywords: 11M06; 11L05; L-functions; Special values; Jordanʼs totient function; Eulerʼs totient function; Mean square average; Gauss sums; Ramanujan sums;
Bounding ζ(s) in the critical strip
Keywords: 11M06; Riemann zeta-function; Extremal functions; Exponential type;
The Fourier inversion and the Riemann functional equation
Keywords: 11M06; 11M26; 11M36; 11M99Riemann hypothesis; Zeta function; Critical strip; Critical line; Functional equation; Mellin transform; Convolution-type products; Fourier inversion formula
An efficient algorithm for the Hurwitz zeta and related functions
Keywords: 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: 11M06; 11M35; 33B15; Hurwitz zeta function; Riemann zeta function; Polygamma function; Lerch zeta function; Series representation; Integral representation; Generalized harmonic numbers;
On differences of zeta values
Keywords: 11M06; 30B50; 39A05; 41A60Riemann zeta function; Finite differences; Asymptotic analysis; Saddle point method; Li's criterion
On the Cohen–Olivier algorithm for computing ζ(s)ζ(s): Error analysis in the real case for an arbitrary precision
Keywords: 65Gxx; 33F05; 11M06; 11Y16Error analysis; Arbitrary precision; Certified precision; Riemann zeta-function
Numerical approximation to ζ(2n+1)ζ(2n+1)
Keywords: 11M06; 11Y35; 41A10; 65D15Riemann zeta function; Bernoulli polynomial; Dirichlet series; Apéry's constant