Counting Hecke eigenforms with nonvanishing \(L\) value

Authors

  • M Manickam Indian Institute of Science Education and Research Bhopal
  • V. Kumar Murty University of Toronto
  • E. M. Sandeep

Keywords:

modular L-function, cusp forms, integral weight, full modular group, Non-vanishing of L-functions

Abstract

We develop some asymptotics for a kernel function introduced by Kohnen and use them to

estimate the number of normalised Hecke eigenforms in $S_k(\Gamma_0(1))$ whose $L$-values

are simultaneously non-vanishing at a given pair of points each of which lies inside the critical strip.

Published

2022-07-22

Issue

Vol. 106 No. 1 (2022)

Section

Articles
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