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On the Hurwitz—Lerch zeta-function
Aequationes Mathematicae, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S Kanemitsu
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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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, 2003 The Lerch zeta-function is the first monograph on this topic, which is a generalization of the classic Riemann, and Hurwitz zeta-functions. Although analytic results have been presented previously in various monographs on zeta-functions, this is the ...
Antanas Laurinčikas +1 more
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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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