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

Davide Schipani

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

Number Theory 2011-02-07 v3

Authors: Davide Schipani

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 $(0,1)$ .

Keywords

Hurwitz zeta function zeros interval (0,1) negative values classical zeta function

Cite

@article{arxiv.1003.2060,
  title  = {Zeros of the Hurwitz zeta function in the interval (0,1)},
  author = {Davide Schipani},
  journal= {arXiv preprint arXiv:1003.2060},
  year   = {2011}
}

Comments

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

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