Results 131 to 140 of about 2,094 (162)

Formulas for the Riemann zeta-function and certain Dirichlet series

Integral Transforms and Special Functions, 2018
Using known theta identities and formulas of S. Ramanujan and G. Hardy among others we prove several formulas for the Riemann zeta-function and two Dirichlet series.
P. Panzone
semanticscholar   +3 more sources

On the joint universality for Dirichlet series connected to periodic zeta-functions

Quaestiones Mathematicae. Journal of the South African Mathematical Society, 2023
In the paper, we consider a collection of absolutely convergent Dirichlet series which in the mean are close to periodic and periodic Hurwitz zeta-functions, and prove that the shifts of mentioned Dirichlet series approximate simultaneously a wide class ...
A. Laurinčikas
semanticscholar   +1 more source

ON A FORMULA FOR THE REGULARIZED DETERMINANT OF ZETA FUNCTIONS WITH APPLICATION TO SOME DIRICHLET SERIES

, 2020
In this paper, we study a large class of zeta functions. We evaluate explicitly the special values of these zeta functions and the associated derivatives at $0$.
Mounir Hajli
semanticscholar   +1 more source

An extension of Maass theory to general Dirichlet series

Integral transforms and special functions, 2022
In this paper we establish the modular relation for Maass forms to the effect that the Fourier–Whittaker expansion and the ramified functional equation are equivalent, i.e. the RHB (Riemann–Hecke–Bochner) correspondence.
Xiaohui Wang, Nianwei Wang, Kanemitsu Shigeru   +2 more
semanticscholar   +1 more source

A two-variable Dirichlet series and its applications

Quaestiones Mathematicae. Journal of the South African Mathematical Society, 2020
We define a two-variable Dirichlet series associated with two arithmetic functions, which is related to the Riemann zeta function, the Dirichlet L-function, the Dirichlet series associated to the harmonic numbers, and truncated multiple zeta functions ...
M. Cenkci, Abdurrahman Ünal
semanticscholar   +1 more source

ON THE APPROXIMATE FUNCTIONAL EQUATION FOR ζ²(s) AND OTHER DIRICHLET SERIES

The Quarterly Journal of Mathematics, 1986
Writing the approximate functional equation for \(\zeta(s)^2\) as \[ \zeta(s)^2=S(s,x)+\chi(s)^2 S(1-s,y)+R(s,x), \] where \(S(s,x)=\sum_{n\leq x}d(n)n^{-\sigma}\), \(xy=\tau^2\), \(\tau =t/2\pi\) and \(\chi(s)=2^s \pi^{s-1} \sin(\pi s/2) \Gamma(1-s),\) the author proves that, if \(0\leq \sigma \leq 1\), \(t\geq 10\) and \(1\leq x,y\leq \tau^2\), then \
openaire   +2 more sources

Probabilistic Multiple-Integral Evaluation of Odd Dirichlet Beta and Even Zeta Functions and Proof of Digamma-Trigamma Reflections

Foundations
The aim of this work was to construct explicit expressions for the summation of Dirichlet Beta functions with odd arguments and Zeta functions with even arguments.
Antonio E. Bargellini, D. Ritelli, G. Spaletta   +2 more
semanticscholar   +1 more source

Zeta functions enumerating subforms of quadratic forms

Mathematische Annalen
In this paper, we introduce and study the Dirichlet series enumerating (proper) equivalence classes of full rank subforms/sublattices of a given quadratic form/lattice, focusing on the positive definite binary case.
Daejun Kim, Seok Hyeong Lee, Seungjai Lee   +2 more
semanticscholar   +1 more source

Mellin Transform of Weierstrass Zeta Function and Integral Representations of Some Lambert Series

Mathematics
We consider a series which combines two Dirichlet series constructed from the coefficients of a Laurent series and derive a general integral representation of the series as a Mellin transform.
Namhoon Kim
semanticscholar   +1 more source

Approximation of analytic functions by an absolutely convergent Dirichlet series

Archiv der Mathematik, 2021
A. Laurinčikas
semanticscholar   +1 more source