The Digit Principle

Keith Conrad

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arXiv · math/0002026

The Digit Principle

Keith Conrad

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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.

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Keith Conrad. 2000-02-03. The Digit Principle. https://arxiv.org/abs/math/0002026

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