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

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Iwaniec and Sarnak showed that at the minimum 25% of L-values associated to holomorphic newforms of fixed even integral weight and level N → ∞ do not vanish at the critical point when N is square-free and ϕ(N) N. In this paper we extend the given result to the case of prime power level N=pν, ν≥ 2.