微分代数在算术函数代数独立性中的应用
数论
2017-01-18 v3
摘要
我们通过Ax关于微分Schanuel猜想的定理，推广并统一了关于算术函数和狄利克雷级数代数独立性的若干结果的证明。在此过程中，我们找到了文献中某些结果的反例。
引用
@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}
}
备注
(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