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}
}
  • M. Nathanson
  • Published in
    Unusual Applications of…
    2000
  • Mathematics, Computer Science
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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References

A functional equation arising from multiplication of quantum integers
Abstract For the quantum integer [n]q=1+q+q2+⋯+qn−1 there is a natural polynomial multiplication such that [m]q⊗q[n]q=[mn]q. This multiplication leads to the functional equation fm(q)fn(qm)=fmn(q),Expand