On the central critical value of the triple product L-function

Abstract

We compute the central critical value of the triple product $L$-function associated to three cusp forms $f_1,f_2,f_3$ with trivial character for groups ${\Gamma }_0(N_i)$ with square free levels $N_i$ not all of which are $1$ and weights $k_i$ satisfying $k_1\ge k_2\ge k_3$ and $k_1<k_2+k_3$. This generalizes work of Gross and Kudla and gives an alternative classical proof of their results in the case $N_1=N_2=N_3$ with $k_1=k_2=k_3=2$.

Cited by in corpus (5)

• Equidistribution of cusp forms in the level aspect
• Arithmetic and equidistribution of measures on the sphere
• Lowest weight modules of Sp_4(R) and nearly holomorphic Siegel modular forms
• On Deligne's conjecture for certain automorphic $L$-functions for $\mathrm{GL}(3)\times \mathrm{GL}(2)$
• Averages and nonvanishing of central values of triple product $L$-functions