Semidirect Products and Functional Equations for Quantum Multiplication
Number Theory
2007-05-23 v1 Quantum Algebra
Abstract
The quantum integer [n]_q is the polynomial 1 + q + q^2 + ... + q^{n-1}, and the sequence of polynomials { [n]_q }_{n=1}^{\infty} is a solution of the functional equation f_{mn}(q) = f_m(q)f_n(q^m). In this paper, semidirect products of semigroups are used to produce families of functional equations that generalize the functional equation for quantum multiplication.
Cite
@article{arxiv.math/0611619,
title = {Semidirect Products and Functional Equations for Quantum Multiplication},
author = {Melvyn B. Nathanson},
journal= {arXiv preprint arXiv:math/0611619},
year = {2007}
}
Comments
7 pages