$p$-adic hypergeometric function related with $p$-adic multiple polylogarithms
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866914051481665536 |
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| author | Furusho, Hidekazu |
| author_facet | Furusho, Hidekazu |
| contents | This paper introduces a $p$-adic analogue of Gauss's hypergeometric function, constructed via a method that is distinct from distinct from Dwork's approach. The idea of our construction is motivated by the Ohno-Zagier formula, which is elucidated through the relationship between the hypergeometric differential equation and the Knizhnik-Zamolodchikov (KZ) equation. We develop a rigorous framework for the residue-wise analytic prolongation of our $p$-adic hypergeometric function by exploring its relationship with $p$-adic multiple polylogarithms. Through a detailed analysis of its local behavior near the point $1$, we show a $p$-adic version of Gauss hypergeometric theorem for the function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_07155 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | $p$-adic hypergeometric function related with $p$-adic multiple polylogarithms Furusho, Hidekazu Number Theory Algebraic Geometry Primary 11S80, Secondary 12H25, 33C05 This paper introduces a $p$-adic analogue of Gauss's hypergeometric function, constructed via a method that is distinct from distinct from Dwork's approach. The idea of our construction is motivated by the Ohno-Zagier formula, which is elucidated through the relationship between the hypergeometric differential equation and the Knizhnik-Zamolodchikov (KZ) equation. We develop a rigorous framework for the residue-wise analytic prolongation of our $p$-adic hypergeometric function by exploring its relationship with $p$-adic multiple polylogarithms. Through a detailed analysis of its local behavior near the point $1$, we show a $p$-adic version of Gauss hypergeometric theorem for the function. |
| title | $p$-adic hypergeometric function related with $p$-adic multiple polylogarithms |
| topic | Number Theory Algebraic Geometry Primary 11S80, Secondary 12H25, 33C05 |
| url | https://arxiv.org/abs/2211.07155 |