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Lithuanian Mathematical Journal, 1996
Let \(s= \sigma+it\) be a complex variable, and let \(\mathbb{R}\) and \(\mathbb{Z}\) denote the sets of all real numbers and all integer numbers, respectively. Then the Lerch zeta-function is defined by \[ L(\lambda, \alpha,s) =\sum^\infty_{m=0} {e^{2 \pi i\lambda m} \over (m+ \alpha)^s} \quad \text{for} \quad \sigma>1, \] where \(\lambda \in\mathbb{R}
Garunkštis, R., Laurinčikas, A.
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Let \(s= \sigma+it\) be a complex variable, and let \(\mathbb{R}\) and \(\mathbb{Z}\) denote the sets of all real numbers and all integer numbers, respectively. Then the Lerch zeta-function is defined by \[ L(\lambda, \alpha,s) =\sum^\infty_{m=0} {e^{2 \pi i\lambda m} \over (m+ \alpha)^s} \quad \text{for} \quad \sigma>1, \] where \(\lambda \in\mathbb{R}
Garunkštis, R., Laurinčikas, A.
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Twists of Lerch Zeta-Functions
Lithuanian Mathematical Journal, 2001This paper is on some basic properties of twists of Lerch zeta-functions defined as \[ L(\lambda, \alpha, s, \chi, Q) = \sum_{n=0}^{\infty}{\chi(n+Q)e^{2\pi i\lambda n}\over (n+\alpha)^{s}} \quad (\Re s > 1), \] where \(0 < \alpha\leq 1\), \(\lambda\in \mathbb R\), \(Q\in \mathbb Z\) and \(\chi\) is a Dirichlet character to the modulus \(q\).
Garunkštis, R., Steuding, J.
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On the Hurwitz—Lerch zeta-function
Aequationes Mathematicae, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kanemitsu, Shigeru +2 more
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Approximation of the Lerch Zeta-Function
Lithuanian Mathematical Journal, 2004For \(\sigma > 1\), 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, 2023This 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, 2020Motivated 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, 2001The 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, 2003Let \(01\), is defined by \[ L(\lambda,\alpha,s)=\sum_{n=0}^{\infty}\frac{e^{2 \pi i \lambda n}}{(n+\alpha)^s}.
Garunkštis, R. +2 more
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The Hurwitz Zeta Function and the Lerch Zeta Function
2017In 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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