Zeros of Dirichlet series with periodic coefficients

Eric Saias, Andreas Weingartner

Let $a=(a_n{)}_{n\ge 1}$ be a periodic sequence, $F_a(s)$ the meromorphic continuation of ${\sum }_{n\ge 1}{a}_n/n^s$, and $N_a({\sigma }_1,{\sigma }_2,T)$ the number of zeros of $F_a(s)$, counted wit…