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

A. P. Veselov, J. P. Ward

The behaviour of real zeroes of the Hurwitz zeta function $$\zeta (s,a)=\sum _{r=0}^{\infty }(a+r{)}^{-s}a>0$$ is investigated. It is shown that $\zeta (s,a)$ has no real zeroes $…