ON THE REDUCTION MODULO $p$ OF MAHLER EQUATIONS - Archive ouverte HAL
Article Dans Une Revue Tohoku mathematical journal Année : 2017

ON THE REDUCTION MODULO $p$ OF MAHLER EQUATIONS

Julien Roques

Résumé

The guiding thread of the present work is the following result, in the vain of Grothendieck's conjecture for differential equations : if the reduction modulo almost all prime $p$ of a given linear Mahler equation with coefficients in $\mathbb{Q}(z)$ has a full set of algebraic solutions, then this equation has a full set of rational solutions. The proof of this result, given at the very end of the paper, relies on intermediate results of independent interest about Mahler equations in characteristic zero as well as in positive characteristic.

Dates et versions

hal-01983117 , version 1 (16-01-2019)

Identifiants

Citer

Julien Roques. ON THE REDUCTION MODULO $p$ OF MAHLER EQUATIONS. Tohoku mathematical journal, 2017, 69 (1), pp.55-65. ⟨10.2748/tmj/1493172128⟩. ⟨hal-01983117⟩
18 Consultations
0 Téléchargements

Altmetric

Partager

More