Diophantine Approximation Groups, Kronecker Foliations and Independence
Number Theory
2019-02-28 v3
Abstract
We introduce diophantine approximation groups and their associated Kronecker foliations, using them to provide new algebraic and geometric characterizations of -linear and algebraic dependence. As a consequence we find reformulations -- as algebraic and geometric (graph) rigidities -- of the Theorems of Baker and Lindemann-Weierstrass, the Logarithm Conjecture and the Schanuel Conjecture. There is an Appendix describing diophantine approximation groups as model theoretic types.
Cite
@article{arxiv.1201.2708,
title = {Diophantine Approximation Groups, Kronecker Foliations and Independence},
author = {T. M. Gendron},
journal= {arXiv preprint arXiv:1201.2708},
year = {2019}
}