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arXiv · 2101.12400

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

Bin Guan
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Abstract

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.

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Bin Guan. 2021-01-29. Averages and nonvanishing of central values of triple product $L$-functions. https://arxiv.org/abs/2101.12400

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