A functional equation arising from multiplication of quantum integers
Melvyn B. Nathanson
Abstract
For the quantum integer [n]q = 1+q+...+qn-1 there is a natural polynomial multiplication *q such that [m]q *q [n]q = [mn]q. This multiplication leads to the functional equation fmn(q) = fm(q)fn(qm), defined on a given sequence (F)=\fn(q)\n=1∞ 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.
Create a lesson
Related papers
An Infinite Family of Apéry-like Recurrences for Euler's Constant
Rotem Kalisch, Tali Monderer, Elyasheev Leibtag et al.
On the saturability of p-adic Lie groups
Casey Perdue
On Divisor Function Polynomials and Dirichlet Series
Martin N. Huxley, Matthew C. Lettington, Karl Michael Schmidt
On a conjecture on Romanoff type representations
Xiao-Hui Yan
Regularization of a Divergent Arithmetic Product via the Asymptotic Monoid: The Case of (-1)ω(n)
A. Alvarez Cruz, E. A. Alvarez Gutierrez
Appell Sequences in Analytic Number Theory: Shifted Expansions and Dirichlet L-Functions
Abdelmejid Bayad