The Second Moment of GL₃ × GL₂ L-functions at Special Points

2025/10/13 by Qi, Zhi
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.11191

Abstract

Let ϕ be a fixed Hecke--Maass form for SL₃ (ℤ) and u_j traverse an orthonormal basis of Hecke--Maass forms for SL₂ (ℤ) . Let 1/4+t_j² be the Laplace eigenvalue of u_j . In this paper, we prove the mean Lindelöf hypothesis for the second moment of L (1/2+it_j, ϕ× u_j) on T < t_j \leqslant T + √(T) . Previously, this was proven by Young on t_j \leqslant T. Our approach is more direct as we do not apply the Poisson summation formula to detect the `Eisenstein--Kloosterman' cancellation.

Citations

• A Bessel delta-method and exponential sums for GL(2)
• A general Voronoi summation formula for GL(n,Z)
• Bounds for GL(3)× GL(2) L-functions and GL(3) L-functions

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