2022/11/17 by Isaac A. Broudy, Broudy, Isaac A., Sebastian Eterović +1
Mathematics · #11F03 #11J81 #11J85 #11J89 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2211.09556
openalex publication_date 2022/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a subfield F of ℂ, we study the linear disjointess of the field E generated by iterated exponentials of elements of F, and the field L generated by iterated logarithms, in the presence of Schanuel's conjecture. We also obtain similar results replacing exp by the modular j-function, under an appropriate version of Schanuel's conjecture, where linear disjointness is replaced by a notion coming from the action of GL2 on ℂ. We also show that for certain choices of F we obtain unconditional versions of these statements.