Finite monodromy of Pochhammer equation

Haraoka, Yoshishige

Annales de l'Institut Fourier, Tome 44 (1994) no. 3, pp. 767-810

We consider the monodromy group $G$ of the Pochhammer differential equation $𝒫$. Let ${𝒫}_p$ be the reduce equation modulo a prime $p$. Then we show that $G$ is finite if and only if ${𝒫}_p$ has a full set of polynomial solutions for almost all primes $p$.

Nous considérons le groupe de monodromie $G$ de l’équation différentielle de Pochhammer $𝒫$. Soit ${𝒫}_p$ l’équation réduite modulo un nombre premier $p$. Alors, on montre que $G$ est fini si et seulement si ${𝒫}_p$ admet un système fondamental de solutions polynomiales pour presque tous les nombres premiers.

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