The Digit Principle
Number Theory
2007-05-23 v1
Abstract
A number of constructions in function field arithmetic involve extensions from linear objects using digit expansions. This technique is described here as a method of constructing orthonormal bases in spaces of continuous functions. We illustrate several examples of orthonormal bases from this viewpoint, and we also obtain a concrete model for the continuous functions on the integers of a local field as a quotient of a Tate algebra in countably many variables.
Keywords
Cite
@article{arxiv.math/0002026,
title = {The Digit Principle},
author = {Keith Conrad},
journal= {arXiv preprint arXiv:math/0002026},
year = {2007}
}
Comments
20 pages, 0 figures, LaTeX, to appear in Journal of Number Theory