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Growth of the Lerch zeta-function [PDF]

Lithuanian Mathematical Journal, 2005
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Ramunas Garunkštis
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Lerch's Theorems over Function Fields

Integers, 2010
AbstractIn this work, we state and prove Lerch's theorems for Fermat and Euler quotients over function fields defined analogously to the number fields.
Yotsanan Meemark, Sirawich Chinwarakorn
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Approximation of the Lerch Zeta-Function

Lithuanian Mathematical Journal, 2004
For \(\sigma > 1\), with real parameters \(\lambda\) and \(\alpha\), \(0 < \alpha \leq 1\), the Lerch zeta--function is defined by \[ L(\lambda, \alpha, s) = \sum_{m=0}^\infty {{e^{2\pi i \lambda m}} \over {(m+\alpha)^s}}, \] and can be continued analytically. Improving on an approximation in the monograph by the author and A.
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An Approximate Functional Equation for the Lerch Zeta Function

Mathematical Notes, 2003
Let \(01\), is defined by \[ L(\lambda,\alpha,s)=\sum_{n=0}^{\infty}\frac{e^{2 \pi i \lambda n}}{(n+\alpha)^s}.
Garunkštis, R., Laurinčikas, A., Steuding, J.   +2 more
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Properties of the Appell–Lerch function (I)

The Ramanujan Journal, 2021
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On Statistical Properties of the Lerch Zeta‐Function

Lithuanian Mathematical Journal, 2001
The Lerch zeta-function with parameters \(01\) by the Dirichlet series \[ L(\lambda,\alpha,s)=\sum_{n=0}^\infty {\exp(2\pi i\lambda)\over (n+\alpha)^s}, \] and by analytic continuation elsewhere except for at most one simple pole at \(s=1\). Being a generalization of the famous Riemann zeta-function \(\zeta(s)=L(1,1,s)\), the value-distribution of the ...
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On universality of the Lerch zeta-function

Proceedings of the Steklov Institute of Mathematics, 2012
It is known that the Lerch zeta-function L(λ, α, s) with transcendental parameter α is universal in the Voronin sense; i.e., every analytic function can be approximated by shifts L(λ, α, s + iτ) uniformly on compact subsets of some region. In this paper, the universality for some classes of composite functions F(L(λ, α, s)) is obtained.
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The universality of the Lerch zeta-function

Lithuanian Mathematical Journal, 1997
Es sei \(0< \lambda< 1\), \(\alpha\) sei eine transzendente Zahl, und \(L(\lambda, \alpha,s)\) \((s\in \mathbb{C})\) bezeichne die Lerchsche Zetafunktion. Ferner sei \(D= \{s\in \mathbb{C}: \frac 12< \operatorname {Re}(s)< 1\}\), und \(\operatorname {mes}M\) sei das Lebesguemaß einer Lebesgue-meßbaren Menge \(M\subset \mathbb{R}\).
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The Lerch function and the thermodynamical functions of the ideal quantum gases

Journal of Mathematical Physics, 2004
The unified description of the main thermodynamical functions of the Bose and Fermi ideal gases, obtained by Lee [J. Math. Phys. 36, 1217 (1995)] in terms of the polylogarithmic functions, can also be obtained by analytic continuation in the chemical potential owing to the analytic properties of the Lerch function that is simply related to the ...
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The Lerch zeta-function. III

2002
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