Applications of differential algebra to algebraic independence of arithmetic functions
Number Theory
2017-01-18 v3
Abstract
We generalize and unify the proofs of several results on algebraic in- dependence of arithmetic functions and Dirichlet series by a theorem of Ax on differential Schanuel conjecture. Along the way, we find counter-examples to some results in the literature.
Keywords
Cite
@article{arxiv.1504.03263,
title = {Applications of differential algebra to algebraic independence of arithmetic functions},
author = {Wai Yan Pong},
journal= {arXiv preprint arXiv:1504.03263},
year = {2017}
}
Comments
(v.2) General improvements on the presentation. Corrected some mistakes in the proof of Theorem~5.5 in the first version. (v.3) Added an addendum showing that the assumption on continuity of derivations (with respect to the norm topology) of our results can be dropped