Dwork Congruences and reflexive Polytopes

2009/11/04 by Kira Samol, Samol, Kira, Duco van Straten +1 · 5 citations
Arts and Humanities · Mathematics · #11G25 #11Sxx #11Y70 #14G10 #14Qxx #Algebraic Geometry (math.AG) #FOS: Mathematics #Linguistics and Discourse Analysis #Number Theory (math.NT) #math.AG #math.NT #msc:11G25 #msc:11Sxx #msc:11Y70 #msc:14G10 #msc:14Qxx

paper · pdf · doi:10.48550/arxiv.0911.0797

arxiv created 2009/11/04 · openalex publication_date 2009/11/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 a key role in the explicit p-adic analytic continuation of the unit root.

Citations

• Notes on Calabi-Yau ordinary differential equations

Cited by

• Partial Lucas-type congruences
• Lucas' theorem: its generalizations, extensions and applications (1878--2014)
• A-hypergeometric series associated to a lattice polytope with a unique interior lattice point
• Algebraic independence of G-functions and congruences "à la Lucas"
• Modular-type functions attached to Calabi-Yau varieties: integrality properties

Related

• Dwork's congruences for the constant terms of powers of a Laurent\n polynomial
• Partial Lucas-type congruences
• Automated Discovery and Proof of Congruence Theorems for Partial Sums of\n Combinatorial Sequences
• Generalised power series determined by linear recurrence relations
• A note on arithmetic congruences