Distribution of the Hessian values of Gaussian hypergeometric functions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912230667190272 |
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| author | Ono, Ken Pujahari, Sudhir Saad, Hasan Saikia, Neelam |
| author_facet | Ono, Ken Pujahari, Sudhir Saad, Hasan Saikia, Neelam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16349 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distribution of the Hessian values of Gaussian hypergeometric functions Ono, Ken Pujahari, Sudhir Saad, Hasan Saikia, Neelam Number Theory 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. |
| title | Distribution of the Hessian values of Gaussian hypergeometric functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2405.16349 |