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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2022 Volume 112, Issue 6, Pages 1003–1016 (Mi mzm13832)

This article is cited in 1 paper

Papers published in the English version of the journal

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

A. Varchenkoab

a Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599-3250 USA
b Faculty of Mathematics and Mechanics, Lomonosov Moscow State University, Moscow, 119991 Russia

Abstract: We consider an example of the joint system of dynamical differential equations and qKZ difference equations with parameters corresponding to equations for elliptic integrals. We solve this system of equations modulo any power $p^n$ of a prime integer $p$. We show that the $p$-adic limit of these solutions as $n\to\infty$ determines a sequence of line bundles, each of which is invariant with respect to the corresponding dynamical connection, and that the sequence of line bundles is invariant with respect to the corresponding qKZ difference connection.

Keywords: Dynamical and qKZ equations, $p^s$-hypergeometric solution, master polynomial, Dwork congruence.

Received: 10.05.2022
Revised: 31.07.2022

Language: English


 English version:
Mathematical Notes, 2022, 112:6, 1003–1016

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© Steklov Math. Inst. of RAS, 2024