Periods of Abelian Varieties, Hypergeometric Functions and Trancedence, pp. 561-587
Authors: (Pierre-Antoine Desrousseaux, Univ. des Sciences et Technologie de Lille-Lille)
Abstract: Hypergeometric functions often appeared in Number Theory. These are transcendental functions, that means that, most of the time, they take transcendental values at algebraic points. Thus, it is interresting, on the one hand, to know the conditions for algebraic values and their consequences, and on the other hand, to understand why particular hypergeometric functions takes a lot of algebraic values. The specificity of hypergeometric functions is that they can be related, thanks to complex integrals, to geometric objects : abelian varieties. Some properties of the abelian varieties imply the expected results for hypergeometric functions.