Ax-Schanuel for the j-function
Logic
2017-02-22 v2 Number Theory
Abstract
In this paper we prove a functional transcendence statement for the j-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 j-function are governed by modular relations.
Keywords
Cite
@article{arxiv.1412.8255,
title = {Ax-Schanuel for the j-function},
author = {Jonathan Pila and Jacob Tsimerman},
journal= {arXiv preprint arXiv:1412.8255},
year = {2017}
}
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