In this paper we prove a functional transcendence statement for the -function which is an analogue of the Ax–Schanuel theorem for the exponential function. It asserts, roughly, that atypical algebraic relations among functions and their compositions with the -function are governed by modular relations.
"Ax–Schanuel for the -function." Duke Math. J. 165 (13) 2587 - 2605, 15 September 2016. https://doi.org/10.1215/00127094-3620005