Asymptotics to all orders of the Hurwitz zeta function
نویسندگان
چکیده
منابع مشابه
New Result of Analytic Functions Related to Hurwitz Zeta Function
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.
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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Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at non-positive integers of the q-analogue of the Hurwitz zeta function, and to study the classical limit of this qanalogue. All the discussion developed here is entirely ...
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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A number of authors have considered mean values of powers of the modulus of the Hurwitz zeta function ζ(s, a), see [3, 4, 5, 6, 7]. In this paper, the mean of the function itself is considered. First a functional equation relating the Riemann zeta function to sums of the values of the Hurwitz zeta function at rational values of a is derived. This functional equation underlies the vanishing of t...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2018
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2018.05.012