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Sato-Tate distribution of p-adic hypergeometric functions
Recently Ono, Saad and the second author [21] initiated a study of value distribution of certain families of Gaussian hypergeometric functions over large finite fields. They investigated two families of Gaussian hypergeometric functions and showed that they satisfy semicircular and Batman distributi...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9708806/ https://www.ncbi.nlm.nih.gov/pubmed/36468936 http://dx.doi.org/10.1007/s40993-022-00414-w |
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author | Pujahari, Sudhir Saikia, Neelam |
author_facet | Pujahari, Sudhir Saikia, Neelam |
author_sort | Pujahari, Sudhir |
collection | PubMed |
description | Recently Ono, Saad and the second author [21] initiated a study of value distribution of certain families of Gaussian hypergeometric functions over large finite fields. They investigated two families of Gaussian hypergeometric functions and showed that they satisfy semicircular and Batman distributions. Motivated by their results we aim to study distributions of certain families of hypergeometric functions in the p-adic setting over large finite fields. In particular, we consider two and six parameters families of hypergeometric functions in the p-adic setting and obtain that their limiting distributions are semicircular over large finite fields. In the process of doing this we also express the traces of pth Hecke operators acting on the spaces of cusp forms of even weight [Formula: see text] and levels 4 and 8 in terms of p-adic hypergeometric function which is of independent interest. These results can be viewed as p-adic analogous of some trace formulas of [1, 2, 6]. |
format | Online Article Text |
id | pubmed-9708806 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-97088062022-12-01 Sato-Tate distribution of p-adic hypergeometric functions Pujahari, Sudhir Saikia, Neelam Res Number Theory Research Recently Ono, Saad and the second author [21] initiated a study of value distribution of certain families of Gaussian hypergeometric functions over large finite fields. They investigated two families of Gaussian hypergeometric functions and showed that they satisfy semicircular and Batman distributions. Motivated by their results we aim to study distributions of certain families of hypergeometric functions in the p-adic setting over large finite fields. In particular, we consider two and six parameters families of hypergeometric functions in the p-adic setting and obtain that their limiting distributions are semicircular over large finite fields. In the process of doing this we also express the traces of pth Hecke operators acting on the spaces of cusp forms of even weight [Formula: see text] and levels 4 and 8 in terms of p-adic hypergeometric function which is of independent interest. These results can be viewed as p-adic analogous of some trace formulas of [1, 2, 6]. Springer International Publishing 2022-11-29 2023 /pmc/articles/PMC9708806/ /pubmed/36468936 http://dx.doi.org/10.1007/s40993-022-00414-w Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Research Pujahari, Sudhir Saikia, Neelam Sato-Tate distribution of p-adic hypergeometric functions |
title | Sato-Tate distribution of p-adic hypergeometric functions |
title_full | Sato-Tate distribution of p-adic hypergeometric functions |
title_fullStr | Sato-Tate distribution of p-adic hypergeometric functions |
title_full_unstemmed | Sato-Tate distribution of p-adic hypergeometric functions |
title_short | Sato-Tate distribution of p-adic hypergeometric functions |
title_sort | sato-tate distribution of p-adic hypergeometric functions |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9708806/ https://www.ncbi.nlm.nih.gov/pubmed/36468936 http://dx.doi.org/10.1007/s40993-022-00414-w |
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