A Bessel δ-method and hybrid bounds for GL₂

2020/08/22 by Yilan Fan, Fan, Yilan, Qingfeng Sun +1
Mathematics · #11F37 #11F66 #11L07 #11M41 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2008.09871

openalex publication_date 2020/08/22 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Let g be a primitive holomorphic or Maass newform for Γ₀(D). In this paper, by studying the Bessel integrals associated to g, we prove an asymptotic Bessel δ-identity associated to g. Among other applications, we prove the following hybrid subconvexity bound L(1/2+it,g⊗ χ)≪_g,ε (q(1+|t|))^εq^3/8(1+|t|)^1/3 for any ε>0, where χ\bmod q is a primitive Dirichlet character with (q, D)=1. This improves the previous known result.

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