Ghosts and congruences for $p^s$-approximations of hypergeometric periods
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| author | Varchenko, Alexander Zudilin, Wadim |
| author_facet | Varchenko, Alexander Zudilin, Wadim |
| contents | We prove general Dwork-type congruences for constant terms attached to tuples of Laurent polynomials. We apply this result to establishing arithmetic and $p$-adic analytic properties of functions originating from polynomial solutions modulo $p^s$ of hypergeometric and KZ equations, solutions which come as coefficients of master polynomials and whose coefficients are integers. As an application we show that the simplest example of a $p$-adic KZ connection has an invariant line subbundle while its complex analog has no nontrivial subbundles due to the irreducibility of the monodromy group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_08548 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Ghosts and congruences for $p^s$-approximations of hypergeometric periods Varchenko, Alexander Zudilin, Wadim Number Theory Mathematical Physics Algebraic Geometry Classical Analysis and ODEs Combinatorics We prove general Dwork-type congruences for constant terms attached to tuples of Laurent polynomials. We apply this result to establishing arithmetic and $p$-adic analytic properties of functions originating from polynomial solutions modulo $p^s$ of hypergeometric and KZ equations, solutions which come as coefficients of master polynomials and whose coefficients are integers. As an application we show that the simplest example of a $p$-adic KZ connection has an invariant line subbundle while its complex analog has no nontrivial subbundles due to the irreducibility of the monodromy group. |
| title | Ghosts and congruences for $p^s$-approximations of hypergeometric periods |
| topic | Number Theory Mathematical Physics Algebraic Geometry Classical Analysis and ODEs Combinatorics |
| url | https://arxiv.org/abs/2107.08548 |