JOINT UNIVERSALITY OF HURWITZ ZETA-FUNCTIONS
نویسندگان
چکیده
منابع مشابه
Joint universality of periodic zeta-functions: continuous and discrete cases
In this paper, we give a survey on universality theorems of the collection of various zeta-functions, when one of them has an Euler product and other has no. We present some results on both, continuous and discrete, cases.
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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).
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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...
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By using a linear operator, we obtain some new results for a normalized analytic function f defined by means of the Hadamard product of Hurwitz zeta function. A class related to this function will be introduced and the properties will be discussed.
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2012
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972712000342