A conjecture for the regularized fourth moment of Eisenstein series

JOURNAL OF NUMBER THEORY

卷:182

Article

Djankovic, Goran¹  Khan, Rizwanur² 

[1] Univ Belgrade, Fac Math, Studentski Trg 16,Pp 550, Belgrade 11000, Serbia

[2] Texas A&M Univ Qatar, POB 23874, Doha, Qatar

关键词: Automorphic forms;    Eisenstein series;    Equidistribution;    L-4-norm;    Regularized inner products;    Quantum chaos;    Random wave conjecture;    L-functions;   

DOI  :  10.1016/j.jnt.2017.06.012

来源: Elsevier

【 摘 要 】

We formulate a version of the Random Wave Conjecture for the fourth moment of Eisenstein series which is based on Zagier's regularized inner product. We prove an asymptotic formula expressing the regularized fourth moment as a mean value of L-functions. This is an advantage over previous work in the literature, which has approached the fourth moment problem through truncated Eisenstein series and not yielded a suitable expression in terms of L-functions. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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