The Hurwitz Zeta Function as a Convergent Series
نویسندگان
چکیده
منابع مشابه
Hypergeometric Series Associated with the Hurwitz-lerch Zeta Function
The present work is a sequel to the papers [3] and [4], and it aims at introducing and investigating a new generalized double zeta function involving the Riemann, Hurwitz, Hurwitz-Lerch and Barnes double zeta functions as particular cases. We study its properties, integral representations, differential relations, series expansion and discuss the link with known results.
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We investigate a few types of generalizations of the Hurwitz zeta function, written Z(s, a) in this abstract, where s is a complex variable and a is a parameter in the domain that depends on the type. In the easiest case we take a ∈ R, and one of our main results is that Z(−m, a) is a constant times Em(a) for 0 ≤ m ∈ Z, where Em is the generalized Euler polynomial of degree n. In another case, ...
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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: Rocky Mountain Journal of Mathematics
سال: 2006
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181069411