Criterion for the integrality of the Taylor coefficients of mirror maps in several variables
| Autor: | Eric Delaygue |
|---|---|
| Přispěvatelé: | Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
Factorial
Pure mathematics Mathematics(all) Generalization Differential equation Mathematics::Number Theory General Mathematics 01 natural sciences Combinatorics 0103 physical sciences FOS: Mathematics Number Theory (math.NT) 0101 mathematics 010306 general physics Mathematics Variable (mathematics) Formal power series Series (mathematics) Mathematics - Number Theory 010102 general mathematics Function (mathematics) Congruence relation [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] Integrality GKZ hypergeometric series Mirror maps |
| Zdroj: | Advances in Mathematics Advances in Mathematics, Elsevier, 2013, 234, pp.414-452 |
| ISSN: | 0001-8708 1090-2082 |
| Popis: | International audience; We give a necessary and sufficient condition for the integrality of the Taylor coefficients at the origin of formal power series $q_i({\mathbf z})=z_i\exp(G_i({\mathbf z})/F({\mathbf z}))$, with ${\mathbf z}=(z_1,...,z_d)$ and where $F({\mathbf z})$ and $G_i({\mathbf z})+\log(z_i)F({\mathbf z})$, $i=1,...,d$ are particular solutions of certain A-systems of differential equations. This criterion is based on the analytical properties of Landau's function (which is classically associated with the sequences of factorial ratios) and it generalizes the criterion in the case of one variable presented in "Critére pour l'intégralité des coefficients de Taylor des applications miroir" [J. Reine Angew. Math.]. One of the techniques used to prove this criterion is a generalization of a version of a theorem of Dwork on the formal congruences between formal series, proved by Krattenthaler and Rivoal in "Multivariate $p$-adic formal congruences and integrality of Taylor coefficients of mirror maps" [arXiv:0804.3049v3, math.NT]. This criterion involves the integrality of the Taylor coefficients of new univariate mirror maps listed in "Tables of Calabi--Yau equations" [arXiv:math/0507430v2, math.AG] by Almkvist, van Enckevort, van Straten and Zudilin. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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