Minimal algebraic solutions of the sixth equation of Painlev\'e
Mathematical Physics
2025-04-14 v1 Complex Variables
math.MP
Abstract
For each of the forty-eight exceptional algebraic solutions of the sixth equation of Painlev\'e, we build the algebraic curve of a degree conjectured to be minimal, then we give an optimal parametric representation of it. This degree is equal to the number of branches, except for fifteen solutions.
Keywords
Cite
@article{arxiv.2504.08287,
title = {Minimal algebraic solutions of the sixth equation of Painlev\'e},
author = {Robert Conte},
journal= {arXiv preprint arXiv:2504.08287},
year = {2025}
}
Comments
19 pages, no figure, to appear, Theoretical and mathematicalphysics