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On real zeros of the Hurwitz zeta function [PDF]

Journal of Number Theory, 2023
In this paper, we present results on the uniqueness of the real zeros of the Hurwitz zeta function in given intervals. The uniqueness in question, if the zeros exist, has already been proved for the intervals $(0,1)$ and $(-N, -N+1)$ for $N \geq 5$ by ...
Karin Ikeda
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Asymptotic expansions for the alternating Hurwitz zeta function and its derivatives [PDF]

Journal of Mathematical Analysis and Applications, 2021
Let $$ \zeta_E(s,q)=\sum_{n=0}^\infty\frac{(-1)^n}{(n+q)^{s}} $$ be the alternating Hurwitz (or Hurwitz-type Euler) zeta function. In this paper, we obtain the following asymptotic expansion of $\zeta_{E}(s,q)$ $$ \zeta_E(s,q)\sim\frac12 q^{-s}+\frac14sq^
Su Hu, Min-Soo Kim
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Moments of the Hurwitz zeta function on the critical line

Mathematical Proceedings of the Cambridge Philosophical Society, 2022
We study the moments $M_k(T;\,\alpha) = \int_T^{2T} |\zeta(s,\alpha)|^{2k}\,dt$ of the Hurwitz zeta function $\zeta(s,\alpha)$ on the critical line, $s = 1/2 + it$ with a rational shift $\alpha \in \mathbb{Q}$ . We conjecture, in analogy with the
A. Sahay
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On the Mishou Theorem for Zeta-Functions with Periodic Coefficients

Mathematics, 2023
Let a={am} and b={bm} be two periodic sequences of complex numbers, and, additionally, a is multiplicative. In this paper, the joint approximation of a pair of analytic functions by shifts (ζnT(s+iτ;a),ζnT(s+iτ,α;b)) of absolutely convergent Dirichlet ...
Aidas Balčiūnas, Mindaugas Jasas, Renata Macaitienė, Darius Šiaučiūnas   +3 more
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LINEAR COMBINATIONS OF HURWITZ ZETA-FUNCTIONS

Kyushu Journal of Mathematics, 2022
As it is well known, the Hurwitz zeta-function, for \(\sigma>1\) and a parameter \(\alpha ...
Steuding, Rasa, Steuding, Jörn
openaire   +1 more source

On a Dirichlet Series Connected to a periodic Hurwitz zeta-function with Transcendental and rational parameter

Mathematical Modelling and Analysis, 2023
In the paper, we construct an absolutely convergent Dirichlet series which in the mean is close to the periodic Hurwitz zeta-function, and has the universality property on the approximation of a wide class of analytic functions.
A. Balčiūnas, A. Laurinčikas, M. Stoncelis   +2 more
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C-polynomials and LC-functions: towards a generalization of the Hurwitz zeta function [PDF]

The Ramanujan journal, 2022
Let f(t)=∑n=0+∞Cf,nn!tn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(
Lahcen Lamgouni
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Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and Evaluation

Journal of Mathematics, 2022
We consider a Hurwitz-Lerch zeta function Φs,z,a sum over the natural numbers. We provide an analytically continued closed form solution for this sum in terms of the addition of Hurwitz-Lerch zeta functions.
Robert Reynolds, Allan Stauffer
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Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function

Mathematics, 2021
We apply our simultaneous contour integral method to an infinite sum in Prudnikov et al. and use it to derive the infinite sum of the Incomplete gamma function in terms of the Hurwitz zeta function.
Robert Reynolds, Allan Stauffer
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On the Hurwitz zeta function with an application to the beta-exponential distribution

Journal of Inequalities and Applications, 2020
We prove a monotonicity property of the Hurwitz zeta function which, in turn, translates into a chain of inequalities for polygamma functions of different orders.
Julyan Arbel, Olivier Marchal, Bernardo Nipoti   +2 more
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