Hybrid bounds on twisted L-functions associated with modular forms

JOURNAL OF NUMBER THEORY

卷:189

Article

Kuan, Chan Ieong¹ 

[1] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Guangdong, Peoples R China

关键词: Holomorphic cusp forms;    Subconvexity;    Hybrid bounds;    Automorphic forms;    Lindelof hypothesis;   

DOI  :  10.1016/j.jnt.2018.02.002

来源: Elsevier

【 摘 要 】

For f a primitive holomorphic cusp form of even weight k >= 4, evel N, and chi a Dirichlet character mod Q with (Q, N) = 1, we establish the following subconvex hybrid bound for t is an element of R, L (1/2 + it, f(chi)) << Q(3/8 + theta/4 + epsilon)(1 + vertical bar t vertical bar)(1/3-2 theta+epsilon), where theta is the best bound toward the Ramanujan-Petersson conjecture at the infinite place. The implied constant only depends on f and epsilon. This is done via amplification and taking advantage of a shifted convolution sum of two variables as defined and analyzed in [9]. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free