Solutions of equations involving the modular $j$ function
Number Theory
2020-02-14 v3 Algebraic Geometry
Logic
Abstract
Inspired by work done for systems of polynomial exponential equations, we study systems of equations involving the modular function. We show general cases in which these systems have solutions, and then we look at certain situations in which the modular Schanuel conjecture implies that these systems have generic solutions. An unconditional result in this direction is proven for certain polynomial equations on with algebraic coefficients.
Cite
@article{arxiv.1907.09858,
title = {Solutions of equations involving the modular $j$ function},
author = {Sebastian Eterović and Sebastián Herrero},
journal= {arXiv preprint arXiv:1907.09858},
year = {2020}
}
Comments
25 pages. Proposition 4.1 has been modified. The proof of Proposition 10.1 has been corrected. Other minor changes have been implemented in order to improve the presentation