A functional equation arising from multiplication of quantum integers

Melvyn B. Nathanson

A functional equation arising from multiplication of quantum integers

Number Theory 2016-12-30 v3 Quantum Algebra

Authors: Melvyn B. Nathanson

Abstract

For the quantum integer $[n]_q = 1+q+...+q^{n-1}$ there is a natural polynomial multiplication $*_q$ such that $[m]_q *_q [n]_q = [mn]_q$ . This multiplication leads to the functional equation $f_{mn}(q) = f_m(q)f_n(q^m),$ defined on a given sequence $\mathcal(F)=\{f_n(q)\}_{n=1}^{\infty}$ of polynomials. This paper contains various results concerning the classification and construction of polynomial sequences that satisfy the functional equation, as well as a list of open problems that arise fromthe classification.

Keywords

q-series and q-analogues finite fields rational functions

Cite

@article{arxiv.math/0203217,
  title  = {A functional equation arising from multiplication of quantum integers},
  author = {Melvyn B. Nathanson},
  journal= {arXiv preprint arXiv:math/0203217},
  year   = {2016}
}

Comments

LaTeX. 18 pages. Revised with minor corrections. To appear in the Journal of Number Theory

A functional equation arising from multiplication of quantum integers

Abstract

Keywords

Cite

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