Number Theory

    

Lindemann-Weierstrass Theorem for Thakur Hyergeometric Functions

Authors: David Adam, Laurent Denis

n 1995, Thakur introduced analogues of hypergeometric functions for Fq [T ]. In this article, we show that the exceptional set of such a function is trivial. This confirms a conjecture stated by Thakur and his co-authors in 2008. Furthermore, we prove a Lindemann-Weierstrass-type theorem for an uncountable class of functions containing hypergeometric functions. The method used allows us to obtain the first transcendence measures (of quality comparable to that of characteristic 0) for values u200bu200bat algebraic arguments of these functions. Finally, in the last section, we exhibit the first infinite families of hypergeometric functions whose exceptional set can be shown to be trivial in the P-adic domain.

Comments: 21 Pages. In French

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[v1] 2025-05-23 20:12:06

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