Submission date: 30 September 2020

Abstract:

We give three equivalent characterisations of the natural closure operator on a field equipped with functions replicating the algebraic behaviour of the modular j-function and its derivatives, following similar work on exponential fields. As an application of these results, we give unconditional cases of a theorem of Eterović-Herrero on the Existential Closedness problem for the complex j-function which previously assumed the modular version of Schanuel's conjecture.

Mathematics Subject Classification: 12H05, 11F03, 03C60

Keywords and phrases:

Full text arXiv 2010.00102: pdf, ps.