On Zeros of Periodic Zeta Functions

Abstract

We consider zeta functions ζ(s; $\mathfrak{a}$ ) given by Dirichlet series with multiplicative periodic coefficients and prove that, for some classes of functions F , the functions F(ζ(s; $\mathfrak{a}$ )) have infinitely many zeros in the critical strip. For example, this is true for sin(ζ(s; $\mathfrak{a}$ )).