On Simultaneous Non-Vanishing of Twisted L-Fnctions Associated to Newforms on T0(N)

Abstract

Given two normalized Hecke eigenforms f1, f2 of weight k1 and k2 respectively of squarefree level N, we consider the product of twisted L-functions associated with f1 and f2 by a quadratic charater χ, and show that if this product does not vanish at the center of the critical strip s = 1/2, then it does not vanish for infinitely many such twists. This is a generalisation of the work due to R. Munshi (J. Number Theory, 132, 666-674 [2012]) for the full modular group to the case of any congruence subgroup of squarfree level N.