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arXiv · 2107.08548

Ghosts and congruences for $p^s$-approximations of hypergeometric periods

Alexander Varchenko·Wadim Zudilin
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Abstract

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.

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BibTeXRIS

Alexander Varchenko, Wadim Zudilin. 2021-07-18. Ghosts and congruences for $p^s$-approximations of hypergeometric periods. https://doi.org/10.1017/s1446788723000083

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