Quantum integers and cyclotomy
Alexander Borisov, Yang Wang, Melvyn B. Nathanson
Abstract
A sequence of functions fn(q)n=1∞ satisfies the functional equation for multiplication of quantum integers if fmn(q) = fm(q)fn(qm) 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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