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## Search Articles

2011, Annals of mathematics studies, ISBN 9780691150659, Volume no. 175, xii, 158

Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function...

Weyl groups | Dirichlet series | Mathematics

Weyl groups | Dirichlet series | Mathematics

Book

2012, 2012, Progress in mathematics, ISBN 9780817683337, Volume 300., viii, 361

Book

3.
Full Text
A fresh approach to classical Eisenstein series and the newer Hilbert–Eisenstein series

International journal of number theory, ISSN 1793-0421, 05/2017, Volume 13, Issue 4, pp. 885 - 911

...–Eisenstein series
r
(
z
)
, introduced by Michael Hauss in 1995. The latter turns out to be the product of the hyperbolic sinh function with an explicit closed form linear combination of digamma functions...

Hilbert-Eisenstein series | Hilbert transform | Butzer-Flocke-Hauss complete Omega function | Bernoulli numbers | digamma function | Eisenstein series | Riemann Zeta function | Dirichlet Eta function | exponential generating functions | Conjugate Bernoulli numbers | Physical Sciences | Mathematics | Science & Technology | Hyperbolic functions

Hilbert-Eisenstein series | Hilbert transform | Butzer-Flocke-Hauss complete Omega function | Bernoulli numbers | digamma function | Eisenstein series | Riemann Zeta function | Dirichlet Eta function | exponential generating functions | Conjugate Bernoulli numbers | Physical Sciences | Mathematics | Science & Technology | Hyperbolic functions

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 01/2021, Volume 493, Issue 2, p. 124541

We prove that for any convergent Laurent series f(z)=∑n=−k∞anzn with k≥0, there is a meromorphic function F...

Zeta function | Dirichlet series | Special functions | Lerch transcendent | Mellin transforms | Power series | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Zeta function | Dirichlet series | Special functions | Lerch transcendent | Mellin transforms | Power series | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

2016, Volume 679

General theory of linear operators | Other Dirichlet series and zeta functions | Completeness of eigenfunctions, eigenfunction expansions | Analytic functions | Functions of a complex variable | Partial differential equations | Spaces and algebras of analytic functions | Cyclic vectors, hypercyclic and chaotic operators | Bounded analytic functions | Spectral theory and eigenvalue problems | Operator theory | Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) | Special classes of linear operators | Bergman spaces, Fock spaces | Analytic spaces | Zeta and $L$-functions: analytic theory | Number theory

Conference Proceeding

Analysis (Wiesbaden), ISSN 0174-4747, 08/2016, Volume 36, Issue 3, pp. 205 - 210

Many Dirichlet series are either continuable to the whole complex plane or admit half-planes as their maximal domain of meromorphic continuation...

Riemann zeta function | Dirichlet series | 11M41 | 30B40 | meromorphic continuation

Riemann zeta function | Dirichlet series | 11M41 | 30B40 | meromorphic continuation

Journal Article

The Rocky Mountain journal of mathematics, ISSN 0035-7596, 1/2014, Volume 44, Issue 2, pp. 443 - 477

The Stieltjes constants 𝛾𝑘(𝑎) appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function ζ(𝑠, 𝑎) about...

Dirichlet L functions | Stirling numbers of the first kind | Stieltjes constants | Lerch zeta function | Riemann zeta function | Laurent expansion | Hurwitz zeta function | Physical Sciences | Mathematics | Science & Technology | 11M35 | 05A10 | 11Y60 | 11M06

Dirichlet L functions | Stirling numbers of the first kind | Stieltjes constants | Lerch zeta function | Riemann zeta function | Laurent expansion | Hurwitz zeta function | Physical Sciences | Mathematics | Science & Technology | 11M35 | 05A10 | 11Y60 | 11M06

Journal Article

Pacific journal of mathematics, ISSN 0030-8730, 03/2006, Volume 224, Issue 1, pp. 185 - 200

We introduce a general method for obtaining the main zeta invariants for a class of double series of Dirichlet type and we apply it to the case of homogeneous...

Kronecker limit formula | Zeta functions | Dirichlet series | Physical Sciences | Mathematics | Science & Technology

Kronecker limit formula | Zeta functions | Dirichlet series | Physical Sciences | Mathematics | Science & Technology

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 6/2018, Volume 186, Issue 2, pp. 215 - 233

We study Dirichlet series enumerating orbits of Cartesian products of maps whose orbit distributions are modelled on the distributions of finite index subgroups of free abelian groups of finite rank...

11M41 | Orbit Dirichlet series | 30B50 | 37P35 | Hadamard products of rational generating functions | Mathematics | Natural boundaries | Igusa functions | 37C30 | local functional equations | Mathematics, general | 05A19 | Multiset permutations | Carlitz’s q -Eulerian polynomials | 05A15 | Carlitz’s q-Eulerian polynomials | Physical Sciences | Science & Technology | Analysis | Orbits | Permutations | Sequences | Functional equations | Dirichlet problem | Polynomials | Combinatorial analysis | Subgroups

11M41 | Orbit Dirichlet series | 30B50 | 37P35 | Hadamard products of rational generating functions | Mathematics | Natural boundaries | Igusa functions | 37C30 | local functional equations | Mathematics, general | 05A19 | Multiset permutations | Carlitz’s q -Eulerian polynomials | 05A15 | Carlitz’s q-Eulerian polynomials | Physical Sciences | Science & Technology | Analysis | Orbits | Permutations | Sequences | Functional equations | Dirichlet problem | Polynomials | Combinatorial analysis | Subgroups

Journal Article

Mathematical modelling and analysis, ISSN 1392-6292, 11/2017, Volume 22, Issue 6, pp. 733 - 749

In the paper, we obtain that certain linear and more general combinations of Dirichlet L-functions and Hurwitz zeta-functions have infinitely many zeros in the critical strip...

universality | Dirichlet L-function | Hurwitz zeta-function | Rouché theorem | Mergelyan theorem | Physical Sciences | Mathematics | Science & Technology | Functions | Research | Functional equations | Mathematical research | Series, Dirichlet | Rouche theorem

universality | Dirichlet L-function | Hurwitz zeta-function | Rouché theorem | Mergelyan theorem | Physical Sciences | Mathematics | Science & Technology | Functions | Research | Functional equations | Mathematical research | Series, Dirichlet | Rouche theorem

Journal Article

Forum mathematicum, ISSN 0933-7741, 03/2012, Volume 24, Issue 2, pp. 239 - 251

It is shown that a broad class of generalized Dirichlet series (including the polylogarithm, related to the Riemann zeta-function...

Dirichlet series and functional equations | Boltzmann equation | functions | Riemann Zeta and | Riemann Zeta and L-functions | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Dirichlet series and functional equations | Boltzmann equation | functions | Riemann Zeta and | Riemann Zeta and L-functions | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Filomat, ISSN 0354-5180, 2016, Volume 30, Issue 7, pp. 1789 - 1799

Journal Article

The Ramanujan journal, ISSN 1382-4090, 5/2018, Volume 46, Issue 1, pp. 91 - 102

With the help of transformation formulas of Dirichlet L-series, we generalize some classical formulas for the values $$\zeta (2N+1)$$
ζ(2N+1)
given by Ramanujan...

Dirichlet L -functions | Fourier Analysis | Eichler integral | 11M99 | Functions of a Complex Variable | Infinite series | Field Theory and Polynomials | Mathematics | Number Theory | Combinatorics | Mellin transform | Dirichlet L-functions | Physical Sciences | Science & Technology | Mellin transforms | Dirichlet problem

Dirichlet L -functions | Fourier Analysis | Eichler integral | 11M99 | Functions of a Complex Variable | Infinite series | Field Theory and Polynomials | Mathematics | Number Theory | Combinatorics | Mellin transform | Dirichlet L-functions | Physical Sciences | Science & Technology | Mellin transforms | Dirichlet problem

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 8/2015, Volume 194, Issue 4, pp. 1015 - 1024

In a recent work on Euler-type formulae for even Dirichlet beta values, i.e.,
$$\beta {(2n)}$$
β
(
2
n
)
, I have derived an exact closed-form expression for a class of zeta series...

Zeta series | 68W30 | Clausen function | 30B50 | Riemann zeta function | Mathematics, general | Mathematics | Dirichlet beta function | 11M06 | 65D15

Zeta series | 68W30 | Clausen function | 30B50 | Riemann zeta function | Mathematics, general | Mathematics | Dirichlet beta function | 11M06 | 65D15

Journal Article

Functiones et approximatio commentarii mathematici, ISSN 0208-6573, 12/2014, Volume 51, Issue 2, pp. 303 - 333

.... We shall also study the analytic continuation of several types of the Dirichlet series related with the circle problem, and study a proof of the functional equation of the Dedekind zeta-function...

The Dedekind zeta-function | The circle problem | Analytic continuation | Periodic Bernoulli functions | analytic continuation | 11N37 | periodic Bernoulli functions | the circle problem | the Dedekind zeta-function

The Dedekind zeta-function | The circle problem | Analytic continuation | Periodic Bernoulli functions | analytic continuation | 11N37 | periodic Bernoulli functions | the circle problem | the Dedekind zeta-function

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2016, Volume 85, Issue 297, pp. 325 - 356

where \chi \operatorname {mod}^* q to the modulus q ]]>

Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

1976, Graduate texts in mathematics, ISBN 354090185X, Volume 41, x, 198

Book

Journal of mathematical analysis and applications, ISSN 0022-247X, 06/2006, Volume 318, Issue 1, pp. 333 - 351

...-analogue of Riemann zeta function, q-analogue Hurwitz zeta function, q-analogue Dirichlet L-function and two-variable q–L-function...

q-Hurwitz zeta function | q-Dirichlet L series | q-Riemann zeta | Dedekind sums | Two-variable L-series | Bernoulli functions | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

q-Hurwitz zeta function | q-Dirichlet L series | q-Riemann zeta | Dedekind sums | Two-variable L-series | Bernoulli functions | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

1990, 2nd ed. --, Graduate texts in mathematics, ISBN 0387971270, Volume 41, x, 204

Book

Applied mathematics and computation, ISSN 0096-3003, 10/2015, Volume 268, pp. 462 - 477

.... We then apply these to the corresponding computation of the Hurwitz zeta function and so of Dirichlet L-series and character polylogarithms.

Lerch transcendent function | Incomplete gamma function | Dirichlet L-series | Character polylogarithms | Polylogarithms | Hurwitz zeta function | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Lerch transcendent function | Incomplete gamma function | Dirichlet L-series | Character polylogarithms | Polylogarithms | Hurwitz zeta function | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

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