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Quantum integers and cyclotomy

Alexander Borisov·Yang Wang·Melvyn B. Nathanson
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Abstract

A sequence of functions {f_n(q)}_{n=1}^{\infty} satisfies the functional equation for multiplication of quantum integers if f_{mn}(q) = f_m(q)f_n(q^m) for all positive integers m and n. This paper describes the structure of all sequences of rational functions with rational coefficients that satisfy this functional equation.

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Alexander Borisov, Yang Wang, Melvyn B. Nathanson. 2003-10-01. Quantum integers and cyclotomy. https://arxiv.org/abs/math/0310005

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