Non-vanishing of Dirichlet series with periodic coefficients

Tapas Chatterjee, M. Ram Murty

For any periodic function $f:\mathbb{N}\to \mathbb{C}$ with period $q$, we study the Dirichlet series $L(s,f):={\sum }_{n\ge 1}f(n)/n^s.$ It is well-known that this admits an ana…