منابع مشابه
On 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...
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 Some Integrals Involving the Hurwitz Zeta Function: Part 2
We establish a series of indefinite integral formulae involving the Hurwitz zeta function and other elementary and special functions related to it, such as the Bernoulli polynomials, ln sin(πq), ln (q) and the polygamma functions. Many of the results are most conveniently formulated in terms of a family of functions Ak (q) := kζ ′(1−k, q), k ∈ N, and a family of polygamma functions of negative ...
متن کاملOn Some Integrals Involving the Hurwitz Zeta Function: Part 2
Abstract. We establish a series of indefinite integral formulae involving the Hurwitz zeta function and other elementary and special functions related to it, such as the Bernoulli polynomials, ln sin(πq), ln Γ(q) and the polygamma functions. Many of the results are most conveniently formulated in terms of a family of functions Ak(q) := kζ (1 − k, q), k ∈ N, and a family of polygamma functions o...
متن کاملThe Critical Values of Generalizations of the Hurwitz Zeta Function
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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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1972
ISSN: 0035-7596
DOI: 10.1216/rmj-1972-2-1-151