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Zeros of the Hurwitz zeta function in the interval (0,1) [PDF]
, 2011 We first give a condition on the parameters $s,w$ under which the Hurwitz zeta function $\zeta(s,w)$ has no zeros and is actually negative. As a corollary we derive that it is nonzero for $w\geq 1$ and $s\in(0,1)$ and, as a particular instance, the known
Schipani, Davide
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A New Family of Zeta Type Functions Involving the Hurwitz Zeta Function and the Alternating Hurwitz Zeta Function [PDF]
Mathematics, 2021 In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by the second author. Applying the Mellin transformation to this generating function, we define a new class of zeta type functions, which is related to the interpolation functions of the Apostol–Bernoulli polynomials, the Bernoulli
Daeyeoul Kim, Yilmaz Simsek
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Hurwitz Zeta Function Is Prime
Mathematics, 2023 We proved that the Hurwitz zeta function is prime. In addition, we derived the Nevanlinna characteristic for this function.
Marius Dundulis +3 more
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On Hurwitz zeta function and Lommel functions [PDF]
International Journal of Number Theory, 2020 We obtain a new proof of Hurwitz’s formula for the Hurwitz zeta function [Formula: see text] beginning with Hermite’s formula. The aim is to reveal a nice connection between [Formula: see text] and a special case of the Lommel function [Formula: see text].
Atul Dixit, Rahul Kumar
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On the periodic Hurwitz zeta-function. [PDF]
Hardy-Ramanujan Journal, 2006 In this paper, an universality theorem in the Voronin sense for the periodic Hurwitz zeta-function is proved.
A. Javtokas, Antanas Laurinčikas
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On the product of Hurwitz zeta-functions [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2017 Corresponding to the lattice point problem for a random sphere Kendall and Rankin [8], Nakajima [9] considered the summatory function of the coefficients of the product of two Hurwitz zeta-functions and obtained the Bessel series expression. In this note we treat the case of the product of $\varkappa$ Hurwitz zeta-functions for an arbitrary integer ...
Wang, Nian Liang, Banerjee, Soumyarup
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Contributions to the theory of the Hurwitz zeta-function [PDF]
Hardy-Ramanujan Journal, 2007 We give various contributions to the theory of Hurwitz zeta-function. An elementary part is the argument relating to the partial sum of the defining Dirichlet series for it; how much can we retrieve the whole from the part. We also give the sixth proof of the far-reaching Ramanujan -- Yoshimoto formula, which is a closed form for the important sum ...
Masami Yoshimoto +3 more
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Integral expressions for Hilbert-type infinite multilinear form and related multiple Hurwitz-Lerch Zeta functions [PDF]
, 2012 The article deals with different kinds integral expressions concerning multiple Hurwitz-Lerch Zeta function (introduced originally by Barnes ), Hilbert-type infinite multilinear form and its power series extension.
Ram K. Saxena, Tibor Pogany
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Zeros of Hurwitz zeta functions [PDF]
Mathematics of Computation, 1976 All complex zeros of each Hurwitz zeta function are shown to lie in a vertical strip. Trivial real zeros analogous to those for the Riemann zeta function are found. Zeros of two particular Hurwitz zeta functions are calculated.
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Closed-form formulae for the derivatives of trigonometric functions at rational multiples of $\pi$ [PDF]
, 2009 In this sequel to our recent note it is shown, in a unified manner, by making use of some basic properties of certain special functions, such as the Hurwitz zeta function, Lerch zeta function and Legendre chi function, that the values of all derivatives ...
Adamchik +6 more
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