English

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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R2 v1 2026-06-22T07:45:30.088Z