On an unconditional \rm GL₃ analog of Selberg's result

2025/02/03 by Qingfeng Sun, Hui Wang, Sun, Qingfeng +1
Mathematics · #Advanced Topics in Algebra #Advanced Algebra and Geometry #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2502.01288

Abstract

Let F be a Hecke--Maass cusp form for SL₃(ℤ) with the Langlands parameter μ_F=(μ_F,1,μ_F,2,μ_F,3) and the associated L-function L(s, F). Define S_F(t)=π^-1arg L(1/2+it, F). When μ_F is in generic position, we establish an unconditional asymptotic formula for the moments of S_F(t). Previously, such a formula was only known to hold under the Generalized Riemann Hypothesis. The key ingredient is a weighted zero-density estimate in the spectral aspect for L(s, F), which has recently been proved by Sun and Wang in arXiv:2412.02416.

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