Large values of L-functions from the Selberg class

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Aistleitner, Christoph¹  Pankowski, Lukasz^2,3 

[1] Graz Univ Technol, Inst Anal & Theory, Steyrergasse 30-2, A-8010 Graz, Austria

[2] Adam Mickiewicz Univ, Fac Math & Comp Sci, Umultowska 87, PL-61614 Poznan, Poland

[3] Nagoya Univ, Grad Sch Math, Nagoya, Aichi 4648602, Japan

关键词: Selberg class;    L-function;    Large values;    Resonance method;    Diophantine approximation;   

DOI  :  10.1016/j.jmaa.2016.08.044

来源: Elsevier

【 摘 要 】

In the present paper we prove lower bounds for L-functions from the Selberg class, by this means improving earlier results obtained by the second author together with Joni Steuding. We formulate two theorems which use slightly different technical assumptions, and give two totally different proofs. The first proof uses the resonance method, which was introduced by Soundararajan, while the second proof uses methods from Diophantine approximation which resemble those used by Montgomery. Interestingly, both methods lead to roughly the same lower bounds, which fall short of those known for the Riemann zeta function and seem to be difficult to be improved. Additionally to these results, we also prove upper bounds for L-functions in the Selberg class and present a further application of a theorem of Chen which is used in the Diophantine approximation method mentioned above. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free