COUNTING HECKE EIGENFORMS WITH NONVANISHING $\boldsymbol {L}$ -VALUE

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 nonvanishing at a given pair of points each of which lies inside the critical strip.

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 2022-08, Vol.106 (1), p.28-47
Main Authors: MANICKAM, M., MURTY, V. KUMAR, SANDEEP, E. M.
Format: Article
Language:English
Subjects:
Hypotheses
Kernel functions
Online Access:Get full text
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Description
Summary: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 nonvanishing at a given pair of points each of which lies inside the critical strip.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972721000927