Not Pfaffian
Number Theory
2021-09-21 v1 Logic
Abstract
This short note describes the connection between strong minimality of the differential equation satisfied by an complex analytic function and the real and imaginary parts of the function being Pfaffian. This connection combined with a theorem of Freitag and Scanlon (2017) provides the answer to a question of Binyamini and Novikov (2017). We also answer a question of Bianconi (2016). We give what seem to be the first examples of functions which are definable in o-minimal expansions of the reals and are differentially algebraic, but not Pfaffian.
Keywords
Cite
@article{arxiv.2109.09230,
title = {Not Pfaffian},
author = {James Freitag},
journal= {arXiv preprint arXiv:2109.09230},
year = {2021}
}