Results 41 to 50 of about 2,163 (157)
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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Series Representations at Special Values of Generalized Hurwitz-Lerch Zeta Function
Abstract and Applied Analysis, 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 ...
S. Gaboury, A. Bayad
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The Lerch Zeta function III. Polylogarithms and special values [PDF]
Research in the Mathematical Sciences, 2016 This paper studies algebraic and analytic structures associated with the Lerch zeta function, extending the complex variables viewpoint taken in part II. The Lerch transcendent $ (s, z, c)$ is obtained from the Lerch zeta function $ (s, a, c)$ by the change of variable $z=e^{2 i a}$.
Lagarias, Jeffrey C. +1 more
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A Generalization of the Secant Zeta Function as a Lambert Series
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 Recently, Lalín, Rodrigue, and Rogers have studied the secant zeta function and its convergence. They found many interesting values of the secant zeta function at some particular quadratic irrational numbers. They also gave modular transformation properties of the secant zeta function.
H.-Y. Li +3 more
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The Lerch zeta function IV. Hecke operators
Research in the Mathematical Sciences, 2016 This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators $\{ T_m: \, m \ge 1\}$ given by $T_m(f)(a, c) = \frac{1}{m} \sum_{k=0}^{m-1} f(\frac{a+k}{m}, mc)$ acting on certain spaces of real-analytic functions, including Lerch zeta functions for various parameter ...
Lagarias, Jeffrey C. +1 more
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The Lerch zeta-function with algebraic irrational parameter
Lietuvos Matematikos Rinkinys, 2009 In this note, we present probabilisticlimit theorems on the complex plane as well as in functional spaces for the Lerch zeta-function with algebraic irrational parameter.
Danutė Genienė
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Joint universality for Lerch zeta-functions
Journal of the Mathematical Society of Japan, 2017 For $01$. In this paper, we prove joint universality for Lerch zeta-functions with distinct $ _1,\ldots, _m$ and transcendental $ $.
LEE, Yoonbok +2 more
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A transformation formula related to Dirichlet L-functions with principal character
Lietuvos Matematikos Rinkinys, 2012 We prove a transformation formula for the function for the exponential sum involving the divisor function. This formula can be applied to obtain meromorphic continuation for the Mellin transform of the square of Dirichlet L-function with principal ...
Aidas Balčiūnas
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On the Density–Density Correlations of the Non‐Interacting Finite Temperature Electron Gas
Contributions to Plasma Physics, Volume 65, Issue 8-9, October 2025.ABSTRACT The density–density correlations of the non‐interacting finite temperature electron gas are discussed in detail. Starting from the ideal linear density response function and utilizing general relations from linear response theory, known and novel expressions are derived for the pair correlation function, static structure factor, dynamic ...
Panagiotis Tolias +2 more
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A short note on a extended finite secant series
AIMS Mathematics, 2023 In this paper, a summation formula for a general family of a finite secant sum has been extended by making use of a particularly convenient integration contour method.
Robert Reynolds
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