Results 41 to 50 of about 2,186 (164)
A limit theorem for the Lerch zeta-function
Lietuvos Matematikos Rinkinys, 2000 There is not abstract.
Jolita Ignatavičiūtė
doaj +3 more sources
Exponential sums of Lerch’s zeta functions [PDF]
Proceedings of the American Mathematical Society, 1985 For x x not an an integer and Re ( s ) > 0 \operatorname {Re} (s) > 0 , let \[ F ( x , s ) = ∑ k = 1 ∞
openaire +2 more sources
On zeros of the Lerch zeta-function. III
Lietuvos Matematikos Rinkinys, 1999 There is not abstract.
Ramūnas Garunkštis
doaj +3 more sources
ON THE ZERO DISTRIBUTIONS OF LERCH ZETA-FUNCTIONS [PDF]
Analysis, 2002 The authors study the distribution of zeros of the Lerch zeta-function \[ L(\lambda,\alpha, s):= \sum^\infty_{n=0} e^{2\pi i\lambda n}(n+\alpha)^{-s}, \] defined by R. Lipschitz in 1857 and further studied by M. Lerch thirty years later, and of its derivative \({\partial\over\partial s} L(\lambda,\alpha, s)\). Let me cite one of the authors' result: If
Garunkštis, Ramūnas, Steuding, Jörn
openaire +2 more sources
On a Certain Extension of the Hurwitz-Lerch Zeta Function
Annals of the West University of Timisoara: Mathematics and Computer Science, 2014 Our purpose in this paper is to consider a generalized form of the extended Hurwitz-Lerch Zeta function. For this extended Hurwitz-Lerch Zeta function, we obtain some classical properties which includes various integral representations, a differential ...
Parmar Rakesh K., Raina R. K.
doaj +1 more source
Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy
, 2020 We initiate the study of Selberg zeta functions $Z_{\Gamma,\chi}$ for geometrically finite Fuchsian groups $\Gamma$ and finite-dimensional representations $\chi$ with non-expanding cusp monodromy.
Fedosova, Ksenia, Pohl, Anke
core +1 more source
On zeros of the derivative of the Lerch zeta-function
Lietuvos Matematikos Rinkinys, 2002 We consider zeros of the derivative of the Lerch zeta-function. We obtain some lower bound for the number of zeros lying on the right from the critical line.
Ramūnas Garunkštis
doaj +3 more sources
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
doaj +1 more source
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
wiley +1 more source
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
openaire +3 more sources