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

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

2010-03-10

arxiv.org/abs/1003.2060v3

Mathematics

Number Theory

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

Scientific paper

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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