Submission date: 25 September 2022

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 j 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.

Mathematics Subject Classification: 11F03 11J89

Keywords and phrases:

Full text arXiv 2209.12192: pdf, ps.