منابع مشابه
On Some Integrals Involving the Hurwitz Zeta
We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Γ(q) and log sin(q).
متن کاملAnalytic continuation of multiple Hurwitz zeta functions
We use a variant of a method of Goncharov, Kontsevich, and Zhao [Go2, Z] to meromorphically continue the multiple Hurwitz zeta function ζd(s; θ) = ∑ 0<n1<···<nd (n1 + θ1) −s1 · · · (nd + θd)d , θk ∈ [0, 1), to C, to locate the hyperplanes containing its possible poles, and to compute the residues at the poles. We explain how to use the residues to locate trivial zeros of ζd(s; θ).
متن کاملMoments of Hypergeometric Hurwitz Zeta Functions
This paper investigates a generalization the classical Hurwitz zeta function. It is shown that many of the properties exhibited by this special function extends to class of functions called hypergeometric Hurwitz zeta functions, including their analytic continuation to the complex plane and a pre-functional equation satisfied by them. As an application, a formula for moments of hypergeometric H...
متن کاملOn Some Definite Integrals Involving the Hurwitz Zeta Function
We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Γ(q) and log sin(q).
متن کاملOn the distribution of zeros of the Hurwitz zeta-function
Assuming the Riemann hypothesis, we prove asymptotics for the sum of values of the Hurwitz zeta-function ζ(s, α) taken at the nontrivial zeros of the Riemann zeta-function ζ(s) = ζ(s, 1) when the parameter α either tends to 1/2 and 1, respectively, or is fixed; the case α = 1/2 is of special interest since ζ(s, 1/2) = (2s − 1)ζ(s). If α is fixed, we improve an older result of Fujii. Besides, we...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2019
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms.12292