Scholarlink

<p>We consider a special family of Gaussian hypergeometric functions whose entries are cubic and trivial characters over finite fields. The special values of these functions are known to give the Frobenius traces of families of Hessian elliptic curves. Using the theory of harmonic Maass forms and mock modular forms, we prove that the limiting distribution of these values is semi-circular (i.e. <i>SU</i>(2)), confirming the usual Sato–Tate distribution in this setting.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Distribution of the Hessian values of Gaussian hypergeometric functions

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年2月17日

查看全文
  • Ken Ono,
  • Sudhir Pujahari,
  • Hasan Saad,
  • Neelam Saikia

摘要

We consider a special family of Gaussian hypergeometric functions whose entries are cubic and trivial characters over finite fields. The special values of these functions are known to give the Frobenius traces of families of Hessian elliptic curves. Using the theory of harmonic Maass forms and mock modular forms, we prove that the limiting distribution of these values is semi-circular (i.e. SU(2)), confirming the usual Sato–Tate distribution in this setting.