Crit\'ere pour l'int\'egralit\'e des coefficients de Taylor des applications miroir
| Autor: | Eric Delaygue |
|---|---|
| Přispěvatelé: | Delaygue, Eric, 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: | 2009 |
| Předmět: |
Mathematics - Number Theory
Applied Mathematics General Mathematics 010102 general mathematics [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG] 01 natural sciences [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] Mathematics - Algebraic Geometry 0103 physical sciences 010307 mathematical physics [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] 0101 mathematics Humanities Mathematics [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT] |
| Zdroj: | Journal für die reine und angewandte Mathematik Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2012, 662, pp.205-252 |
| ISSN: | 0075-4102 1435-5345 |
| Popis: | International audience; We give a necessary and sufficient condition for the integrality of the Taylor coefficients of mirror maps at the origin. By mirror maps, we mean formal power series z.exp(G(z)/F(z)), where F(z) and G(z)+log(z)F(z) are particular solutions of certain generalized hypergeometric differential equations. This criterion is based on the analytical properties of Landau's function (which is classically associated to the sequences of factorial ratios) and it generalizes results proved by Krattenthaler-Rivoal in "On the integrality of the Taylor coefficients of mirror maps" (to appear in Duke Math. J.). One of the techniques used to prove this criterion is a generalization of a theorem of Dwork on the formal congruences between formal series, which proved to be insufficient for our purposes. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|