Results 51 to 60 of about 5,484,622 (180)

Value distribution theorems for the Lerch zeta-function. [PDF]

, 2019
The Lerch zeta-function defined, for sigma greater than 1, by the Dirichlet series and by analytic continuation elsewhere, is investigated. The main attention is devoted to the universality of the Lerch zeta-function i.e., to approximation of analytic ...
Mincevič, Asta,
core  

A Generalization of Ramanujan‐Type Integrals

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
Recently, Xu, Yin, and Zhou obtained explicit evaluations of the Ramanujan‐type integrals ∫0∞xs−1sinbx/coshax−cosbxdx and ∫0∞xs−1sinbx/coshax+cosbxdx, expressing them in closed form in terms of the gamma function, the Riemann zeta function, and the alternating zeta function.
Irshad Ayoob, Shikha Binwal
wiley   +1 more source

The Cotangent Function as an Avatar of the Polylogarithm Function of Order 0 and Ramanujan’s Formula

Axioms
In this paper we will be concerned with zeta-symmetry—the functional equation for the (Riemann) zeta-function (equivalents to which are called modular relations)—and reveal the reason why so many results are intrinsic to PFE (Partial Fraction Expansion ...
Ruiyang Li, Haoyang Lu, Shigeru Kanemitsu   +2 more
doaj   +1 more source

On the mean square of Lerch zeta-functions [PDF]

Archiv der Mathematik, 2003
Für \(01) \] definiert und besitzt eine analytische Fortsetzung in ganz \({\mathbb C}\) bis auf höchstens einen einfachen Pol bei \(s=1\). Aus der bekannten Funktionalgleichung dieser Funktion haben die Verff. eine approximative Funktionalgleichung abgeleitet [An approximate functional equation for the Lerch zeta-function, Math.
Garunkštis, R., Laurinčikas, A., Steuding, J.   +2 more
openaire   +1 more source

Wijsman Statistical, Strong Cesàro, and Ideal Convergence of Closed Sets in Idempotent Bicomplex Metric Spaces

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
This paper studies generalized Wijsman convergence for sequences of nonempty closed subsets of an idempotent bicomplex metric space. Let ρ = d1e1 + d2e2, where d1 and d2 are metrics on the same underlying set X. For a nonempty subset A of X, we define the bicomplex point‐to‐set distance by ρ(x, A) = d1(x, A)e1 + d2(x, A)e2.
Ameni Gargouri, Mehmet Gürdal, Ömer Kişi, Abdelwaheb Mhemdi, Maria Alessandra Ragusa   +4 more
wiley   +1 more source

The Lerch zeta function IV. Hecke operators

Research in the Mathematical Sciences, 2016
This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators $\{ T_m: \, m \ge 1\}$ given by $T_m(f)(a, c) = \frac{1}{m} \sum_{k=0}^{m-1} f(\frac{a+k}{m}, mc)$ acting on certain spaces of real-analytic functions, including Lerch zeta functions for various parameter ...
Lagarias, Jeffrey C., Li, Wen-Ching Winnie   +1 more
openaire   +3 more sources

Explicit height estimates for CM curves of genus 2

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract In this paper, we make explicit the constants of Habegger and Pazuki's work from 2017 on bounding the discriminant of cyclic Galois CM fields corresponding to genus 2 curves with CM and potentially good reduction outside a predefined set of primes. We also simplify some of the arguments.
Linda Frey, Samuel Le Fourn, Elisa Lorenzo García   +2 more
wiley   +1 more source

Inequalities for Lerch transcendent function [PDF]

, 2023
Some fundamental inequalities for Lerch transcendent function with positive terms by utilising certain classical results due to Hölder, Čebyšev, Grüss and others, are established. Some particular cases of interest for Polylogarithm function, Hurwitz zeta
Silvestru Sever Dragomir, Dragomir, Sever S   +1 more
core   +1 more source

On a generalization of the Lerch zeta function [PDF]

Application of a Mellin transform to a series which represents a generalization of the Lerch zeta function yields a transformation series. One obtains the asymptotic behavior of the series, together with some associated expansions and limit relations and
Rivera, Dorothy Marguerite
core   +5 more sources

On the Density–Density Correlations of the Non‐Interacting Finite Temperature Electron Gas

Contributions to Plasma Physics, Volume 65, Issue 8-9, October 2025.
ABSTRACT The density–density correlations of the non‐interacting finite temperature electron gas are discussed in detail. Starting from the ideal linear density response function and utilizing general relations from linear response theory, known and novel expressions are derived for the pair correlation function, static structure factor, dynamic ...
Panagiotis Tolias, Tobias Dornheim, Jan Vorberger   +2 more
wiley   +1 more source