Joint cubic moment of Eisenstein series and Hecke-Maass cusp forms

2024/10/06 by Charng Rang Guo, Guo, Chengliang · 1 citation
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2410.04448

Abstract

Let ψ be a smooth compactly supported function on \mathbbX = SL(2,ℤ)\backslashℍ. In this paper, we are interested in the joint cubic moments of automorphic forms when the spectral parameters go to infinity. We show that the diagonal case for Eisenstein series ∫_\mathbbXψ(z)E(z,1/2+it)³ dμz = O_ψ(t^-1/3+ε). In off-diagonal case we prove (1)/(2log t)∫_\mathbbXψ(z)|E(z,1/2+it)|²g(z)dμz = o(1) as long as min\t , t_g\ → ∞. Finally we show ∫_\mathbbXψ(z)f²(z)g(z)dμz = o(1) in the range |t_f - t_g| ≤ t_f^2/3-ε where f,g are two Hecke-Maass cusp forms.

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• Mixed moments of Hecke eigenforms and L-functions

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