# 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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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 2011 14 Jan 2012 21:05 23 Jan 2022 20:15 Nova Science Publishers 1942-5600 Green https://www.novapublishers.com/catalog/product_info.php?products_id=27468 (Publisher)http://arxiv.org/abs/1003.2060