The Second Moment of Rankin-Selberg L-function and Hybrid Subconvexity Bound

2014/04/08 by Zhilin Ye, Ye, Zhilin · 2 citations
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1404.2336

openalex publication_date 2014/04/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let M,N be coprime square-free integers. Let f be a holomorphic cusp form of level N and g be either a holomorphic or a Maaß form with level M. Using a large sieve inequality, we establish a bound of the form ∑_g|L^(j)(1/2+it,f ⊗ g)|² ≪_t M+M^2/3-βN^4/3 where β≈ 1/500. As a consequence, we obtain subconvexity bounds for L^(j)(1/2+it,f ⊗ g)≪ (MN)^{1/2 - α} for any N

Citations

• Level Aspect Subconvexity For Rankin-Selberg L-functions

Cited by

• Simultaneous non-vanishing of central values of GL(2)× GL(3) and GL(3)× GL(3) L-functions
• Subconvexity for Rankin Selberg L-Functions at Special Points

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