Subconvex bound for \textrmGL(3) × \textrmGL(2) L-functions: \textrmGL(3)-spectral aspect

2020/06/14 by Sumit Kumar, Kumar, Sumit, Mallesham, Kummari +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2006.07819

openalex publication_date 2020/06/14 · openalex created_date 2020/06/19 · openalex updated_date 2026/07/28

Abstract

Let ϕ be a Hecke-Maass cusp form for SL(3, ℤ) with Langlands parameters (\bf t_i)_i=1³ and f be a holomorphic or Hecke-Maass cusp form for SL(2,ℤ). In this article, we prove the following subconvex bound L(ϕ× f, 1/2) ≪_f,ε T ^{(3)/(2)-δ_ξ+ε}, δ_ξ=min\ξ/4, (1-2ξ)/4 \, for the central value L(ϕ× f, 1/2) in the GL(3)-spectral aspect, where (\bf t_i)_i=1³ satisfies |\bf t₃ - \bf t₂| \asymp T^1-ξ, \bf t_i \asymp T, i=1, 2, 3, with ξ a real number such that 0 < ξ<1/2.

Cited by

• Spectral aspect subconvex bounds for \rm U_n+1 × \rm U_n

Related

• Subconvexity bound for GL(3) × GL(2) L-functions in GL(2) spectral aspect
• Subconvexity for GL(3)× GL(2) L-functions in t-aspect
• Subconvexity for GL(3)× GL(2) L-functions in GL(3) spectral aspect
• Uniform bounds for \rm GL(3) × GL(2) L-functions
• On the subconvexity problem for GL(3)× GL(2) L-functions