# Congruences for Hasse--Witt matrices and solutions of $p$-adic KZ equations

@inproceedings{Varchenko2021CongruencesFH, title={Congruences for Hasse--Witt matrices and solutions of \$p\$-adic KZ equations}, author={Alexander Varchenko and Wadim Zudilin}, year={2021} }

We prove general Dwork-type congruences for Hasse–Witt matrices attached to tuples of Laurent polynomials. We apply this result to establishing arithmetic and padic analytic properties of functions originating from polynomial solutions modulo p of Knizhnik–Zamolodchikov (KZ) equations, solutions which come as coefficients of master polynomials and whose coefficients are integers. As an application we show that the p-adic KZ connection associated with the family of hyperelliptic curves y = (t…

## One Citation

### Dynamical and qKZ Equations Modulo $$p^s$$: an Example

- MathematicsMathematical Notes
- 2022

— We consider an example of the joint system of dynamical di ﬀ erential equations and qKZ di ﬀ erence equations with parameters corresponding to equations for elliptic integrals. We solve this system…

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