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arXiv · 1307.3841

Arithmetic Differential Equations of Painleve' VI Type

Alexandru Buium·Yuri I. Manin
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Abstract

Using the description of Paileve' VI family of differential equations in terms of a universal elliptic curve, going back to R. Fuchs (cf. [Ma96]), we translate it into the realm of Arithmetic Differential Equations (cf. [Bu05]), where the role of derivative "in the $p$--adic direction" is played by a version of Fermat quotient

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Alexandru Buium, Yuri I. Manin. 2013-07-15. Arithmetic Differential Equations of Painleve' VI Type. https://arxiv.org/abs/1307.3841

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