Generic Solutions of Equations Involving the Modular $j$-function
Number Theory
2025-02-03 v2 Algebraic Geometry
Logic
Abstract
Assuming a modular version of Schanuel's conjecture and the modular Zilber-Pink conjecture, we show that the existence of generic solutions of certain families of equations involving the modular function can be reduced to the problem of finding a Zariski dense set of solutions. By imposing some conditions on the field of definition of the variety, we are also able to obtain unconditional versions of this result.
Cite
@article{arxiv.2209.12192,
title = {Generic Solutions of Equations Involving the Modular $j$-function},
author = {Sebastian Eterović},
journal= {arXiv preprint arXiv:2209.12192},
year = {2025}
}
Comments
40 pages, minor revisions