Non-vanishing of automorphic L-functions of prime power level

Abstract

Iwaniec and Sarnak showed that at the minimum 25% of L-values associated to holomorphic newforms of fixed even integral weight and level $N\to \infty$ do not vanish at the critical point when N is square-free and $\varphi (N)\sim N$. In this paper we extend the given result to the case of prime power level $N=p^{\nu }$, $\nu \ge 2$.