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

2021/01/29 by Guan, Bin
#11F67 #11F72 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2101.12400

Abstract

Let f,g,h be three normalized cusp newforms of weight 2k on Γ₀(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× g× 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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