Results 141 to 150 of about 2,188 (164)

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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Fractional calculus of the Lerch zeta function – part II

Mathematical Methods in the Applied Sciences, 2023
This paper concerns the fractional derivative of the Lerch zeta function. The author already dealt with its functional equation. He reduced its computational cost and proved an approximate functional equation for this fractional derivative. Here, we study the mean square of this fractional derivative.
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Convolution of values of the Lerch zeta-function

Journal of Number Theory, 2020
Motivated by the very classical ``convolutional'' result of the special depth 2 MZV \[\zeta(n-1,1)=\frac{n-1}{2} \zeta(n)-\frac{1}{2} \sum_{j=2}^{n-2} \zeta(j) \zeta(n-j),\] the authors prove a convolution identity for the Lerch zeta function \[\Phi(z ; \alpha ; s):=\sum_{n=0}^{\infty} \frac{z^{n}}{(n+\alpha)^{s}}.\] The main result is that, under ...
Murty, M. Ram, Pathak, Siddhi
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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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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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The Hurwitz Zeta Function and the Lerch Zeta Function

2017
In this chapter we will discuss formulas we have developed for the evaluation of certain zeta functions. We will need them later for the numerical computation of the spectrum of the transfer operator. The implementations of these zeta functions are in a sense the heart of our computations, so we need to be very careful.
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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 zeta-function. III

2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Statistical Properties of the Lerch Zeta-Function. II

Lithuanian Mathematical Journal, 2002
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 \(s=1\). In the present paper the author proves a discrete limit theorem for the Lerch zeta-function \(L(1,\alpha,s ...
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