The Weyl bound for triple product L-functions

2023/04/05 by Valentin Blomer, Subhajit Jana, Paul D. Nelson · 3 citations
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Finite Group Theory Research

paper · doi:10.1215/00127094-2022-0058

Abstract

Let π1, π2, π3 be three cuspidal automorphic representations for the group SL(2,Z), where π1 and π2 are fixed and π3 has large analytic conductor. We prove a subconvex bound for L(1∕2,π1⊗π2⊗π3) of Weyl-type quality. Allowing π3 to be an Eisenstein series, we also obtain a Weyl-type subconvex bound for L(1∕2+it,π1⊗π2).

Cited by

• Stationary phase analysis for analytic newvectors and application to subconvexity problems
• The Weyl bound for Rankin-Selberg L-functions with Joint Ramification
• Dissipation of correlations of holomorphic cusp forms
• Uniform subconvexity bounds for GL(2)× GL(2) L-functions in the spectral aspect

Related

• The Weyl bound for triple product L-functions in the cubic level
• Bounds for standard L-functions
• On triple product L-functions
• Spectral Reciprocity and Hybrid Subconvexity Bound for triple product L-functions
• The subconvexity bound for triple product L-function in level aspect