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Dwork congruences and reflexive polytopes

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Abstract

We show that the coefficients of the power series expansion of the principal period of a Laurent polynomial satisfy strong congruence properties. These congruences play key role in the explicit p-adic analytic continuation of the unit-root. The methods we use are completely elementary.

Résumé

Nous montrons que les coefficients du développement en série de puissances de la période principale d’un polynôme de Laurent satisfont à de fortes propriétés de congruence. Ces congruences jouent un rôle clé pour le prolongement analytique p-adique explicite sur le disque unité.

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Acknowledgments

We thank A. Mellit for his comments. The work of the first author was funded by the SFB Transregio 45 Mainz–Bonn–Essen.

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Authors and Affiliations

  1. Institut für Mathematik, FB 08 Physik, Mathematik und Informatik, Johannes Gutenberg-Universität, 55099, Mainz, Germany

    Kira Samol & Duco van Straten

Authors
  1. Kira Samol
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  2. Duco van Straten
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Correspondence to Duco van Straten.

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Samol, K., van Straten, D. Dwork congruences and reflexive polytopes. Ann. Math. Québec 39, 185–203 (2015). https://doi.org/10.1007/s40316-015-0031-9

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  • DOI: https://doi.org/10.1007/s40316-015-0031-9

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