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GHOSTS AND CONGRUENCES FOR
$\boldsymbol {p}^{\boldsymbol {s}}$-APPROXIMATIONS OF HYPERGEOMETRIC PERIODS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 116 / Issue 1 / February 2024
- Published online by Cambridge University Press:
- 02 August 2023, pp. 96-127
- Print publication:
- February 2024
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- Article
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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.
