IMSc Webinar

A weighted sum of L-functions of modular forms

Sandeep E. M.

KSOM

This talk would be split into two parts. Aim of the first part is to present a lower bound obtained for $\max_{f}~ |L(f,\sigma)|$ at a given real point $\sigma$ inside the critical strip, where $f$ runs over the Hecke basis for $S_k$, the space of cusp forms of weight $k$ and level 1. In order to obtain this, we develop an asymptotic expansion for certain weighted sum of $L$-functions of cuspidal Hecke eigenforms. In the second part, we discuss certain partial results in relation to the following question: Given $s=\sigma+it$, a complex point inside the critical strip (outside the critical line), can we quantify the number of Hecke eigenforms $f$ in $S_k$ whose $L$-value is non-vanishing at $s$? These are joint works with M. Manickam and V. Kumar Murty.
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