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Special values of generalized multiple Hurwitz zeta functions and their derivatives. Applications towards some Witten zeta functions attached to semi-simple Lie algebras

Simon Rutard
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On the Poincaré expansion of the Hurwitz zeta function

Lithuanian Mathematical Journal, 2021
In this paper, we extend the result of Paris [R.B. Paris, The Stokes phenomenon associated with the Hurwitz zeta function ζ(s, a), Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 461(2053):297–304, 2005] on the exponentially improved expansion of the Hurwitz zeta function ζ(s, z), the expansion of which can be reduced to the large-z Poincare ...
B. Fejzullahu
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On multiple Hurwitz zeta function of Mordell–Tornheim type

International Journal of Number Theory, 2021
We introduce a certain multiple Hurwitz zeta function as a generalization of the Mordell–Tornheim multiple zeta function, and study its analytic properties. In particular, we evaluate the values of the function and its first and second derivatives at non-
K. Onodera
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Zeros of the Riemann zeta-function in the discrete universality of the Hurwitz zeta-function

Studia scientiarum mathematicarum Hungarica (Print), 2020
Let 0 < γ1 < γ2 < ··· ⩽ ··· be the imaginary parts of non-trivial zeros of the Riemann zeta-function. In the paper, we consider the approximation of analytic functions by shifts of the Hurwitz zeta-function ζ(s + iγkh, α), h > 0, with parameter α such ...
A. Laurinčikas
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On the Hurwitz—Lerch zeta-function

Aequationes Mathematicae, 2000
Let \( \Phi(z,s,\alpha) = \sum\limits^\infty_{n = 0} {z^n \over (n + \alpha)^s} \) be the Hurwitz-Lerch zeta-function and \( \phi(\xi,s,\alpha)=\Phi(e^{2\pi i\xi},s,\alpha) \) for \( \xi\in{\Bbb R} \) its uniformization. \( \Phi(z,s,\alpha) \) reduces to the usual Hurwitz zeta-function \( \zeta(s,\alpha) \) when z= 1, and in particular \( \zeta(s ...
Masami Yoshimoto, Masanori Katsurada, Shigeru Kanemitsu   +2 more
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ASYMPTOTIC BEHAVIOR OF THE INVERSE OF TAILS OF HURWITZ ZETA FUNCTION

, 2020
This paper deals with the inverse of tails of Hurwitz zeta function. More precisely, for any positive integer s ≥ 2 and 0 ≤ a < 1, we give an algorithm for finding a simple form of fs,a(n) such ...
Ho-Hyeong Lee, Jong-Do Park
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ON THE UNIVERSALITY OF THE HURWITZ ZETA-FUNCTION

International Journal of Number Theory, 2012
It is known that the Hurwitz zeta-function ζ(s, α) with transcendental or rational parameter α is universal in the sense that its shifts ζ(s + iτ, α), τ ∈ ℝ, approximate with a given accuracy any analytic function uniformly on compact subsets of the strip D = {s ∈ ℂ : ½ < σ < 1}. Let H(D) denote the space of analytic functions on D equipped with
Antanas Laurinčikas, Antanas Laurinčikas   +1 more
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