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A Generalized Bohr–Jessen Type Theorem for the Epstein Zeta-Function

Mathematics, 2022
Let Q be a positive defined n×n matrix and Q[x̲]=x̲TQx̲. The Epstein zeta-function ζ(s;Q), s=σ+it, is defined, for σ>n2, by the series ζ(s;Q)=∑x̲∈Zn\{0̲}(Q[x̲])−s, and is meromorphically continued on the whole complex plane.
Antanas Laurinčikas, Renata Macaitienė
doaj   +3 more sources

A Generalized Discrete Bohr–Jessen-Type Theorem for the Epstein Zeta-Function

Mathematics, 2023
Suppose that Q is a positive defined n×n matrix, and Q[x̲]=x̲TQx̲ with x̲∈Zn. The Epstein zeta-function ζ(s;Q), s=σ+it, is defined, for σ>n2, by the series ζ(s;Q)=∑x̲∈Zn∖{0̲}(Q[x̲])−s, and it has a meromorphic continuation to the whole complex plane. Let
Antanas Laurinčikas, Renata Macaitienė
doaj   +3 more sources

On Epstein's Zeta Function (I) [PDF]

Proceedings of the National Academy of Sciences of the United States of America, 1949
1. \(ax^2+bxy+cy^2\) sei eine definite quadratische Form, also \(\Delta = 4ac-b^2>0\). Für die Zetafunktion \[ \mathsf{Z}(s)=\mathop{{\sum}'} (am^2+bmn+cn^2)^{-s}, \qquad \text{Re}\,s > 1, \] gilt die Formel \[ \mathsf{Z}(s)= 2\zeta(2s)a^{-s}+\frac{2^{2s}a^{s-1}\sqrt{\pi}}{\Gamma(s)\Delta^{s-\frac12}} \zeta(2s-1)\Gamma(s-\frac12)+Q(s) \] mit einer ...
S Chowla, Chowla S
exaly   +4 more sources

A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions

Mathematics
In the paper, we prove a joint limit theorem in terms of the weak convergence of probability measures on C2 defined by means of the Epstein ζ(s;Q) and Hurwitz ζ(s,α) zeta-functions. The limit measure in the theorem is explicitly given.
Hany Gerges, Antanas Laurinčikas, Renata Macaitienė   +2 more
doaj   +3 more sources

Unified Theory of Zeta-Functions Allied to Epstein Zeta-Functions and Associated with Maass Forms

Mathematics, 2023
In this paper, we shall establish a hierarchy of functional equations (as a G-function hierarchy) by unifying zeta-functions that satisfy the Hecke functional equation and those corresponding to Maass forms in the framework of the ramified functional ...
Nianliang Wang, Takako Kuzumaki, Shigeru Kanemitsu   +2 more
doaj   +1 more source

Scalar Particles around a Rindler–Schwarzschild Wormhole

Universe, 2022
In this paper, we study quantum relativistic features of a scalar field around the Rindler–Schwarzschild wormhole. First, we introduce this new class of spacetime, investigating some energy conditions and verifying their violation in a region nearby the ...
C. R. Muniz, H. R. Christiansen, M. S. Cunha, J. Furtado, V. B. Bezerra   +4 more
doaj   +1 more source

Exact continuum representation of long-range interacting systems and emerging exotic phases in unconventional superconductors

Physical Review Research, 2023
Continuum limits are a powerful tool in the study of many-body systems, yet their validity is often unclear when long-range interactions are present.
Andreas A. Buchheit, Torsten Keßler, Peter K. Schuhmacher, Benedikt Fauseweh   +3 more
doaj   +1 more source

On the minima and convexity of Epstein zeta function [PDF]

Journal of Mathematical Physics, 2008
Let Zn(s;a1,…,an) be the Epstein zeta function defined as the meromorphic continuation of the function ∑k∊Zn\{0}(∑i=1n[aiki]2)−s,  Re s>n/2 to the complex plane. We show that for fixed s≠n/2, the function Zn(s;a1,…,an) as a function of (a1,…,an)∊(R+)n with fixed ∏i=1nai has a unique minimum at the point a1=⋯=an.
Lim, S. C., Teo, L. P.
openaire   +4 more sources

On Epstein's Zeta-function.

Journal für die reine und angewandte Mathematik (Crelles Journal), 1967
Summary:
Chowla, S., Selberg, A.
openaire   +1 more source

On the universality of the Epstein zeta function [PDF]

Commentarii Mathematici Helvetici, 2020
We study universality properties of the Epstein zeta function E_n(L,s) for lattices L of large dimension n
Andersson, Johan, Södergren, Carl Anders   +1 more
openaire   +3 more sources