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Some notes on distribution of Hecke eigenvalues for Maass cusp forms

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Abstract

In this paper, we get some results on the distribution of Hecke eigenvalues for Maass cusp forms. We consider the diagonal version of Sato–Tate conjecture, a central limit theorem, and a quantitative result on the Ramanujan conjecture.

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Author information

Authors and Affiliations

  1. College of Mathematics and Statistics, Shenzhen University, Shenzhen, Guangdong, 518060, China

    Yingnan Wang

  2. Faculty of Information Technology, Macau University of Science and Technology, Macau, China

    Xuanxuan Xiao

Authors
  1. Yingnan Wang
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  2. Xuanxuan Xiao
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Corresponding authors

Correspondence to Yingnan Wang or Xuanxuan Xiao.

Additional information

The author is supported by the Natural Science Foundation of China (grant No. 11501376), Guangdong Province Natural Science Foundation (grant No. 2015A030310241), and Natural Science Foundation of Shenzhen University (grant No. 201541) (Yingnan Wang).

The author is supported by Faculty Research Grant of MUST (FRG, grant No. FRG-17-032-FI) and Macau Science and Technology Development Fund (FDCT, grant No. 044/2015/A2) (Xuanxuan Xiao).

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Wang, Y., Xiao, X. Some notes on distribution of Hecke eigenvalues for Maass cusp forms. Lith Math J 57, 521–535 (2017). https://doi.org/10.1007/s10986-017-9377-9

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  • DOI: https://doi.org/10.1007/s10986-017-9377-9

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