On the real zeroes of the Hurwitz zeta-function and Bernoulli polynomials

The behaviour of real zeroes of the Hurwitz zeta-function ζ(s,a)=∑r=0∞(a+r)−s for real positive a is investigated. It is shown that ζ(s,a) has no real zeroes (s=σ,a) in the region a>−σ2πe+14πelog(−σ)+1 for large negative σ. In the region 0