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Zeros of the Hurwitz zeta function in the interval (0,1)


Schipani, D (2011). Zeros of the Hurwitz zeta function in the interval (0,1). Journal of Combinatorics and Number Theory, 3(1):71-74.

Abstract

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 result that the classical zeta function has no zeros in $(0,1)$.

Abstract

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 result that the classical zeta function has no zeros in $(0,1)$.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2011
Deposited On:14 Jan 2012 21:05
Last Modified:17 Feb 2018 14:35
Publisher:Nova Science Publishers
ISSN:1942-5600
OA Status:Green
Related URLs:https://www.novapublishers.com/catalog/product_info.php?products_id=27468 (Publisher)
http://arxiv.org/abs/1003.2060

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