# Formal power series arising from multiplication of quantum integers

@inproceedings{Nathanson2000FormalPS, title={Formal power series arising from multiplication of quantum integers}, author={Melvyn B. Nathanson}, booktitle={Unusual Applications of Number Theory}, year={2000} }

For the quantum integer [n]_q = 1+q+q^2+... + q^{n-1} there is a natural polynomial multiplication such that [mn]_q = [m]_q \otimes_q [n]_q. This multiplication is given by the functional equation f_{mn}(q) = f_m(q) f_n(q^m), defined on a sequence {f_n(q)} of polynomials such that f_n(0)=1 for all n. It is proved that if {f_n(q)} is a solution of this functional equation, then the sequence {f_n(q)} converges to a formal power series F(q).
Quantum mulitplication also leads to the functional… Expand

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