Arithmetic Properties of Mirror Maps Associated with Gauss Hypergeometric Equations
نویسندگان
چکیده
— We draw up the list of Gauss hypergeometric differential equations having maximal unipotent monodromy at 0 whose associated mirror map has, up to a simple rescaling, integral Taylor coefficients at 0. We also prove that these equations are characterized by much weaker integrality properties (of p-adic integrality for infinitely many primes p in suitable arithmetic progressions). It turns out that the mirror maps with the above integrality property have modular origins.
منابع مشابه
On Generalized Hypergeometric Equations and Mirror Maps
This paper deals with generalized hypergeometric differential equations of order n ≥ 3 having maximal unipotent monodromy at 0. We show that, among these equations, those leading to mirror maps with integral Taylor coefficients at 0 (up to simple rescaling) have special parameters, namely R-partitioned parameters. This result yields the classification of all generalized hypergeometric different...
متن کاملArithmetic properties of Schwarz maps
The subject of this article belongs to the general question Under which condition(s) suitably normalized transcendental functions take algebraic values at algebraic arguments? Already the classical examples of Weierstrass’ result concerning the exponential function and Theodor Schneider’s result about the elliptic modular function show that arguments and values in these cases are of particular ...
متن کامل1 v 1 2 7 Ju l 1 99 5 Mirror Maps , Modular Relations and Hypergeometric Series I ⋄ Bong
Motivated by the recent work of Kachru-Vafa in string theory, we study in Part A of this paper, certain identities involving modular forms, hypergeometric series, and more generally series solutions to Fuchsian equations. The identity which arises in string theory is the simpliest of its kind. There are nontrivial generalizations of the identity which appear new. We give many such examples – al...
متن کاملTransformations of Gauss hypergeometric functions
The paper classifies algebraic transformations of Gauss hypergeometric functions and pull-back transformations between hypergeometric differential equations. This classification recovers the classical transformations of degree 2, 3, 4, 6, and finds other transformations of some special classes of the Gauss hypergeometric function.
متن کاملAlgebraic transformations of Gauss hypergeometric functions
This paper classifies algebraic transformations of Gauss hypergeometric functions and pull-back transformations between hypergeometric differential equations. This classification recovers the classical transformations of degree 2, 3, 4, 6, and finds other transformations of some special classes of the Gauss hypergeometric function.
متن کامل