Ax-Schanuel Type Theorems on Functional Transcendence via Nevanlinna Theory
Complex Variables
2019-09-04 v1 Number Theory
Abstract
We will apply Nevanlinna Theory to prove several Ax-Schanuel type Theorems for functional transcendence when the exponential map is replaced by other meromorphic functions. We also show that analytic dependence will imply algebraic dependence for certain classes of entire functions. Finally, some links to transcendental number theory and geometric Ax-Schanuel Theorem will be discussed.
Keywords
Cite
@article{arxiv.1909.01018,
title = {Ax-Schanuel Type Theorems on Functional Transcendence via Nevanlinna Theory},
author = {Jiaxing Huang and Tuen-Wai Ng},
journal= {arXiv preprint arXiv:1909.01018},
year = {2019}
}