Submission date: 9 February 2021

Abstract:

In this paper, we prove several Ax-Schanuel type results for uniformizers of geometric structures. In particular, we give a proof of the full Ax-Schanuel Theorem with derivatives for uniformizers of any Fuchsian group of the first kind and any genus. Our techniques combine tools from differential geometry, differential algebra and the model theory of differentially closed fields. The proof is very similar in spirit to Ax's proof of the theorem in the case of the exponential function.

Mathematics Subject Classification: 11F03, 12H05, 03C60

Keywords and phrases:

Full text arXiv 2102.03384: pdf, ps.