Nonvanishing of L-functions of Cusp Forms inside the Critical Strip
نویسنده
چکیده
A theorem of W. Kohnen states that the generalized Riemann hypothesis (GRH) holds on an average for holomorphic cusp forms on the upper half plane for the full modular group SL2(Z). In this article we prove a couple of generalizations of this theorem of Kohnen that the GRH holds on an average for holomorphic cusp forms on the upper half plane for arbitrary level, weight and primitive nebentypus. The talk I gave in the international conference ANTZETA at IMSc, Chennai, India in January 2002, was on nonvanishing of certain Rankin-Selberg L-functions. This has in the meanwhile appeared with all details in [7]. I take this opportunity to thank the organizers of this conference for inviting me for this short and sweet meeting of which I have many pleasant memories.
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