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GHOSTS AND CONGRUENCES FOR $\boldsymbol {p}^{\boldsymbol {s}}$-APPROXIMATIONS OF HYPERGEOMETRIC PERIODS
Published online by Cambridge University Press: 02 August 2023
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 Knizhnik–Zamolodchikov (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 its monodromy representation.
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- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 116 , Issue 1 , February 2024 , pp. 96 - 127
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
Communicated by Michael Coons
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