On the integrality of the Taylor coefficients of mirror maps

DOI10.1215/00127094-2009-063zbMath1267.11077arXiv0709.1432OpenAlexW2962883687MaRDI QIDQ849197

Christian Krattenthaler, Tanguy Rivoal

Publication date: 25 February 2010

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.1432

Mathematics Subject Classification ID

Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Fourier coefficients of automorphic forms (11F30) Generalized hypergeometric series, ({}_pF_q) (33C20) (p)-adic differential equations (12H25) Mirror symmetry (algebro-geometric aspects) (14J33) Arithmetic mirror symmetry (11G42)

Related Items (18)

On Dwork’s 𝑝-adic formal congruences theorem and hypergeometric mirror maps ⋮ On the integrality of factorial ratios and mirror maps ⋮ On generalized hypergeometric equations and mirror maps ⋮ Modularity of Calabi–Yau Varieties: 2011 and Beyond ⋮ Arithmetic properties of mirror maps associated with Gauss hypergeometric equations ⋮ Renormalization, isogenies, and rational symmetries of differential equations ⋮ A criterion for the integrality of the Taylor coefficients of mirror maps in several variables ⋮ Schwarzian conditions for linear differential operators with selected differential Galois groups ⋮ Integrality of the Taylor coefficients of roots of mirror maps ⋮ Eisenstein type series for Calabi-Yau varieties ⋮ Mirror symmetry for stable quotients invariants ⋮ ANALYTIC PROPERTIES OF MIRROR MAPS ⋮ Algebraic independence for values of integral curves ⋮ Arithmetic properties of hypergeometric mirror maps and Dwork's congruences ⋮ CY-operators and $L$-functions ⋮ Critère pour l'intégralité des coefficients de Taylor des applications miroir ⋮ On the integrality of hypergeometric series whose coefficients are factorial ratios ⋮ Modular forms, Schwarzian conditions, and symmetries of differential equations in physics

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