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Simultaneous non-vanishing of twists

Authors:	Amir Akbary

Institution:	Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive West, Lethbridge, Alberta, Canada T1K 3M4

Abstract:	Let be a newform of even weight , level and character $\psi$ and let be a newform of even weight , level and character $\eta$ . We give a generalization of a theorem of Elliott, regarding the average values of Dirichlet -functions, in the context of twisted modular -functions associated to and . Using this result, we find a lower bound in terms of for the number of primitive Dirichlet characters modulo prime $q\leq Q$ whose twisted product -functions $L_{f,\chi}(s_0) L_{g,\chi}(s_0)$ are non-vanishing at a fixed point $s_0=\sigma_0+it_0$ with $\frac{1}{2}<\sigma_0\leq 1$ .

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