Non-vanishing of the first derivative of GL(3) x GL(2) L-functions

作者：Chen, Guohua^*; Yan, Xiaofei

来源：International Journal of Number Theory, 2018, 14(3): 847-869.

DOI：10.1142/S1793042118500513

• GL(3) x GL(2) Rankin-Selberg L-functions
• non-vanishing
• Kuznetsov formula
• Voronoi formula

Let f be a fixed self-dual Hecke-Maass cusp form for SL(3, Z) and {mu(j)} be an orthogonal basis of odd Hecke-Maass cusp forms for SL(2, Z). We prove an asymptotic formula for the average of the first derivative of the Rankin-Selberg L-function of f and mu(j) at the center point s = 1/2. This implies the non-vanishing results for the first derivative of these L-functions at the center point s = 1/2.

• 出版日期2018-4
• 单位山东师范大学; 山东大学