Hybrid bounds for Rankin-Selberg L-functions

JOURNAL OF NUMBER THEORY

卷:175

Article

Hou, Fei¹  Zhang, Meng² 

[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

[2] Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan 250014, Peoples R China

关键词: Automorphic forms;    Rankin-Selberg convolution;    Subconvexity;   

DOI  :  10.1016/j.jnt.2016.11.009

来源: Elsevier

【 摘 要 】

Let M be a square-free integer and P be a prime such that (P, M) = 1. We prove a new hybrid bound for L(1/2, f circle times g) where f is a primitive holomorphic cusp form of level M and g a primitive (either holomorphic or Maass) cusp form of level P satisfying P similar to M-eta) with 0 < eta < 2/15. Particularly in the range beta < eta < (2 - 32 beta)/15 with beta = 11/4875 we present a strengthened level aspect hybrid subconvexity bound for L(1/2, f circle times g) relative to the current bounds obtained by Holowinsky-Munshi [11] and Ye [27]. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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