Quantum variance for cubic moment of Hecke--Maass cusp forms and Eisenstein series

2025/10/14 by Huang, Bingrong, Li, Liangxun
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.12322

Abstract

In this paper, we give the upper bounds on the variance for cubic moment of Hecke--Maass cusp forms and Eisenstein series respectively. For the cusp form case, the bound comes from a large sieve inequality for symmetric cubes. We also give some nontrivial bounds for higher moments of symmetric cube L-functions. For the Eisenstein series case, the upper bound comes from Lindelöf-on-average type bounds for various L-functions. In particular, we establish the sharp upper bounds for the fourth moment of GL(2)× GL(2) L-functions and the eighth moment of GL(2) L-functions around special points 1/2+it_j. Our proof is based on the work of Chandee and Li \citeC-L20 about bounding the second moment of GL(4)× GL(2) L-functions.

Citations

• The fourth moment of truncated Eisenstein series
• L⁴-norms and sign changes of Maass forms
• L^p-Norm Bounds for Automorphic Forms via Spectral Reciprocity
• Bounds for standard L-functions
• Quantum variance for Eisenstein Series
• On the Random Wave Conjecture for Eisenstein series
• A conjecture for the regularized fourth moment of Eisenstein series
• Upper bounds on L-functions at the edge of the critical strip
• Quantum unique ergodicity for SL₂(Z)\H
• Rankin Triple Products and Quantum Chaos
• Uniform Bound for Hecke L-Functions
• On sums of Hecke series in short itervals
• High moments of the Riemann zeta-function

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• Quantum variance for dihedral Maass forms