# 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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