Results 31 to 40 of about 114 (80)
Twisted Eisenstein series, cotangent‐zeta sums, and quantum modular forms
Transactions of the London Mathematical Society, Volume 7, Issue 1, Page 33-48, December 2020., 2020 Abstract We define twisted Eisenstein series Es±(h,k;τ) for s∈C, and show how their associated period functions, initially defined on the upper half complex plane H, have analytic continuation to all of C′:=C∖R⩽0. We also use this result, as well as properties of various zeta functions, to show that certain cotangent‐zeta sums behave like quantum ...
Amanda Folsom
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Further generalization of the extended Hurwitz-Lerch Zeta functions
Boletim da Sociedade Paranaense de Matemática, 2017 Recently various extensions of Hurwitz-Lerch Zeta functions have been investigated. Here, we first introduce a further generalization of the extended Hurwitz-Lerch Zeta functions. Then we investigate certain interesting and (potentially) useful properties, systematically, of the generalization of the extended Hurwitz-Lerch Zeta functions, for example ...
Rakesh K. Parmar +2 more
openaire +4 more sources
Around the Lipschitz Summation Formula
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 Boundary behavior of important functions has been an object of intensive research since the time of Riemann. Kurokawa, Kurokawa‐Koyama, and Chapman studied the boundary behavior of generalized Eisenstein series which falls into this category. The underlying principle is the use of the Lipschitz summation formula.
Wenbin Li +3 more
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Reflection properties of zeta related functions in terms of fractional derivatives [PDF]
, 2020 We prove that the Weyl fractional derivative is a useful instrument to express certain properties of the zeta related functions. Specifically, we show that a known reflection property of the Hurwitz zeta function ¿(n, a) of integer first argument can be ...
Kohara, A.K., Sesma, J., Ferreira, E.M.
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On some series representations of the Hurwitz zeta function [PDF]
, 2008 A variety of infinite series representations for the Hurwitz zeta function are obtained. Particular cases recover known results, while others are new. Specialization of the series representations apply to the Riemann zeta function, leading to additional ...
Coffey, Mark W.
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Extended Blumberg-Dieckmann Series [PDF]
, 2023 This paper introduces a set of finite summation formulas and utilize them to establish various functional relationships involving the multivariable Hurwitz-Lerch zeta function.
Reynolds, Robert
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New Expansion Formulas for a Family of the λ‐Generalized Hurwitz‐Lerch Zeta Functions
International Journal of Mathematics and Mathematical Sciences, Volume 2014, Issue 1, 2014., 2014 We derive several new expansion formulas for a new family of the λ‐generalized Hurwitz‐Lerch zeta functions which were introduced by Srivastava (2014). These expansion formulas are obtained by making use of some important fractional calculus theorems such as the generalized Leibniz rules, the Taylor‐like expansions in terms of different functions, and ...
H. M. Srivastava +2 more
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An explicit expression of the Lerch zeta function on maximal domains of holomorphy [PDF]
, 2023 We give two results on the Lerch zeta function $\Phi(z,\,s,\,w)$. The first is to give an explicit expression providing both the analytic continuation of $\Phi$ in $n$-variables $(n \in \{1,\,2,\,3\})$ to maximal domains of holomorphy in $\mathbb{C}^n ...
Kozuma, Rintaro
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A Study of a Certain Subclass of Hurwitz‐Lerch‐Zeta Function Related to a Linear Operator
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 By using a linear operator with Hurwitz‐Lerch‐Zeta function, which is defined here by means of the Hadamard product (or convolution), the author investigates interesting properties of certain subclasses of meromorphically univalent functions in the punctured unit disk U*.
F. Ghanim, Mohamed Amal Aouf
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Series Representations at Special Values of Generalized Hurwitz‐Lerch Zeta Function
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 By making use of some explicit relationships between the Apostol‐Bernoulli, Apostol‐Euler, Apostol‐Genocchi, and Apostol‐Frobenius‐Euler polynomials of higher order and the generalized Hurwitz‐Lerch zeta function as well as a new expansion formula for the generalized Hurwitz‐Lerch zeta function obtained recently by Gaboury and Bayad , in this paper we ...
S. Gaboury, A. Bayad, Junesang Choi
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