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Acta Arithmetica

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Distribution of Hecke eigenvalues for holomorphic Siegel modular forms

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi Acta Arithmetica MSC: Primary 11N75; Secondary 11F46 DOI: 10.4064/aa230831-6-5 Published online: 10 July 2024

Abstract

We obtain two results on the distribution of Hecke eigenvalues of holomorphic Siegel modular forms. The first is the average Sato–Tate distribution, and the second is the Gaussian central limit theorem.

Authors

  • Henry H. KimDepartment of Mathematics
    University of Toronto
    Toronto, Ontario M5S 2E4, Canada
    and
    Korea Institute for Advanced Study, Seoul, Korea
    e-mail
  • Satoshi WakatsukiFaculty of Mathematics and Physics
    Institute of Science and Engineering
    Kanazawa University
    Kanazawa, Ishikawa, 920-1192, Japan
    e-mail
  • Takuya YamauchiMathematical Institute
    Tohoku University
    Sendai 980-8578, Japan
    e-mail
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