Differential equations, mirror maps and zeta values

Abstract

The aim of this work is an analytic investigation of differential equations producing mirror maps as well as giving new examples of mirror maps; one of these examples is related to (rational approximations to) $\zeta (4)$. We also indicate certain observations that might become a subject of further research.

AmSTeX, 38 pages

References in corpus (4)

• Tables of Calabi--Yau equations
• Sums of squares of binomial coefficients, with applications to Picard-Fuchs equations
• Dynamical zeta functions and Kummer congruences
• Binomial sums related to rational approximations to $\zeta (4)$

Cited by in corpus (16)

• Tables of Calabi--Yau equations
• Ising n-fold integrals as diagonals of rational functions and integrality of series expansions
• Quadratic transformations and Guillera's formulae for $1/{\pi }^2$
• Monodromy calculatons of fourth order equations of Calabi-Yau type
• Eisenstein type series for Calabi-Yau varieties
• Multivariate $p$-adic formal congruences and integrality of Taylor coefficients of mirror maps
• The Geometry of Gauged Linear Sigma Model Correlation Functions
• GLSMs, joins, and nonperturbatively-realized geometries
• Analytic Periods via Twisted Symmetric Squares
• New representations for all sporadic Apéry-like sequences, with applications to congruences
• On genus one fibered Calabi-Yau threefolds with 5-sections
• Smoothing Calabi-Yau toric hypersurfaces using the Gross-Siebert algorithm
• The art of finding Calabi-Yau differential eq1uations
• 5-th order differential equations related to Calabi-Yau differential equations
• Differential algebra on lattice Green functions and Calabi-Yau operators (unabridged version)
• Démonstration de l'Observation 2 d'Almkvist et Zudilin