Tohoku Mathematical Journal, Second Series
Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735
ON THE REDUCTION MODULO $p$ OF MAHLER EQUATIONS
Julien Roques
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キーワード: Mahler equations
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2017 年 69 巻 1 号 p. 55-65

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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.

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