# Ax–Schanuel for the $j$-function

@article{Pila2016AxSchanuelFT,
title={Ax–Schanuel for the \$j\$-function},
author={J. Pila and Jacob Tsimerman},
journal={Duke Mathematical Journal},
year={2016},
volume={165},
pages={2587-2605}
}
• Published 2016
• Mathematics
• Duke Mathematical Journal
• 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.
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