The MHS algebra and supercongruences

Abstract

A supercongruence is a congruence between rational numbers modulo a power of a prime. In this paper, we give a technique for finding and algorithmically proving supercongruences by expressing terms as infinite series involving certain generalizations of the harmonic numbers. We apply the technique to derive many new supercongruences. We also provide software for finding and proving supercongruences using our technique.

31 pages, comments are welcome. Part of v1 of this paper is now a separate submission: "The completed finite period map and Galois theory of supercongruences",arXiv:1703.04248

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• p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation
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Cited by in corpus (1)

• Sequential periods of the crystalline Frobenius