On Zeros of Periodic Zeta Functions - Laurinčikas, A.; Šiaučiūnas, D. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
We consider zeta functions ζ(s; \( a \) ) given by Dirichlet series with multiplicative periodic coefficients and prove that, for some classes of functions F , the functions F(ζ(s; \( a \) )) have infinitely many zeros in the critical strip. For example, this is true for sin(ζ(s; \( a \) )).