Arithmetic Differential Equations of Painleve' VI Type
Number Theory
2013-12-19 v2
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 --adic direction" is played by a version of Fermat quotient
Cite
@article{arxiv.1307.3841,
title = {Arithmetic Differential Equations of Painleve' VI Type},
author = {Alexandru Buium and Yuri I. Manin},
journal= {arXiv preprint arXiv:1307.3841},
year = {2013}
}
Comments
27 pages. A typo corrected