Zeros of the Hurwitz zeta function in the interval (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 $w\ge 1$ and $s\in (0,1)$ and, as a particular instance, the known result that the classical zeta function has no zeros in $(0,1)$.

Some reformulation done. Accepted for publication in Journal of Combinatorics and Number Theory

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