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arXiv · 1610.07269

A Note on Average of Roots of Unity

Chatchawan Panraksa·Pornrat Ruengrot
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Abstract

We consider the problem of characterizing all functions $f$ defined on the set of integers modulo $n$ with the property that an average of some $n$th roots of unity determined by $f$ is always an algebraic integer. Examples of such functions with this property are linear functions. We show that, when $n$ is a prime number, the converse also holds. That is, any function with this property is representable by a linear polynomial. Finally, we give an application of the main result to the problem of determining self perfect isometries for the cyclic group of prime order $p$.

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Chatchawan Panraksa, Pornrat Ruengrot. 2016-10-24. A Note on Average of Roots of Unity. https://arxiv.org/abs/1610.07269

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