Uniform bounds for \rm GL(3) × GL(2) L-functions

2021/04/27 by Bingrong Huang, Huang, Bingrong
Mathematics · Social Sciences · #Analytic Number Theory Research #FOS: Mathematics #Historical Geopolitical and Social Dynamics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2104.13025

openalex publication_date 2021/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove uniform bounds for \rm GL (3)× GL(2) L-functions in the \rm GL(2) spectral aspect and the t aspect by a delta method. More precisely, let ϕ be a Hecke--Maass cusp form for \rm SL(3,ℤ) and f a Hecke--Maass cusp form for \rm SL(2,ℤ) with the spectral parameter t_f. Then for t∈ℝ and any ε>0, we have L(1/2+it,ϕ× f) ≪_ϕ,ε (t_f+|t|)^27/20+ε. Moreover, we get subconvexity bounds for L(1/2+it,ϕ× f) whenever |t|-t_f ≫ (|t|+t_f)^3/5+ε.

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