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arXiv:2101.12400 [math.NT]AbstractReferencesReviewsResources

Averages and nonvanishing of central values of triple product $L$-functions

Bin Guan

Published 2021-01-29Version 1

Let $f,g,h$ be three normalized cusp newforms of weight $2k$ on $\Gamma_0(N)$ which are eigenforms of Hecke operators. We use Ichino's period formula combined with a relative trace formula to show exact averages of $L(3k-1,f\times g\times h)$. We also present some applications of the average formulas to the nonvanishing problem, giving a lower bound on the number of nonvanishing central $L$-values when one of the forms is fixed.

Categories: math.NT
Subjects: 11F67, 11F72
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