Quantitative versions of the joint distributions of Hecke eigenvalues

JOURNAL OF NUMBER THEORY

卷:169

Article

Tang, Hengcai¹  Wang, Yingnan² 

[1] Henan Univ, Inst Modern Math, Sch Math & Informat Sci, Kaifeng 475004, Henan, Peoples R China

[2] Shenzhen Univ, Coll Math & Stat, Shenzhen 518060, Guangdong, Peoples R China

关键词: Holomorphic cusp forms;    Maass cusp forms;    Hecke eigenvalues;    Joint distribution;    Quantitative version;   

DOI  :  10.1016/j.jnt.2016.05.011

来源: Elsevier

【 摘 要 】

In 2009, Omar and Mazhouda proved that as k -> infinity , {lambda(f) (p(2)) : f is an element of H-k} and {lambda(f) (p(3)) : f is an element of H-k} are equidistributed with respect to some measures respectively, where H-k is the set of all the normalized primitive holomorphic cusp forms of weight k for SL2(Z). In this paper, we obtain a quantitative version of Omar and Mazhouda's result. Moreover, we find out that {lambda(f) (p(4)) : f is an element of H-k} and {lambda(f) (p(r)) - lambda(f) (p(r-2)) : f is an element of H-k and r >= 2} follow some nice distribution laws respectively as k -> infinity and get quantitative versions of these distributions. In the context of Maass cusp forms, we establish analogous results. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free