On the ring of approximation triples attached to a class of extremal real numbers

Details On the ring of approximation triples attached to a class of extremal real numbers On the ring of approximation triples attached to a class of extremal real numbers

2008-04-05

arxiv.org/abs/0804.0865v1

Mathematics

Number Theory

24 pages

Scientific paper

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.

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