On the ring of approximation triples attached to a class of extremal real numbers
Number Theory
2013-01-07 v1 Combinatorics
Abstract
We attach a ring of sequences to each number from a certain class of extremal real numbers, and we study the properties of this ring both from an analytic point of view by exhibiting elements with specific behaviors, and also from an algebraic point of view by identifying it with the quotient of a polynomial ring over Q. The link between these points of view relies on combinatorial results of independent interest. We apply this theory to estimate the dimension of a certain space of sequences satisfying prescribed growth constrains.
Keywords
Cite
@article{arxiv.0804.0865,
title = {On the ring of approximation triples attached to a class of extremal real numbers},
author = {Damien Roy and Eric Villani},
journal= {arXiv preprint arXiv:0804.0865},
year = {2013}
}
Comments
24 pages