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Journal of the Ramanujan Mathematical Society

Volume 34, Issue 2, June 2019  pp. 245–252.

On simultaneous non-vanishing of twisted L-functions associated to newforms on Γ0(N)

Authors:  Abhash Kumar Jha, Abhishek Juyal and Manish Kumar Pandey
Author institution:Department of Mathematics, Indian Institute of science, Bangalore 560 012, India

Summary:  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.

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