Loading...
Please wait, while we are loading the content...
Similar Documents
Quadratic addition rules for quantum integers
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kontorovich, Alex Nathanson, Melvyn B. |
| Copyright Year | 2005 |
| Abstract | Abstract For every positive integer n , the quantum integer [ n ] q is the polynomial [ n ] q = 1 + q + q 2 + ⋯ + q n - 1 . A quadratic addition rule for quantum integers consists of sequences of polynomials R ′ = { r n ′ ( q ) } n = 1 ∞ , S ′ = { s n ′ ( q ) } n = 1 ∞ , and T ′ = { t m , n ′ ( q ) } m , n = 1 ∞ such that [ m + n ] q = r n ′ ( q ) [ m ] q + s m ′ ( q ) [ n ] q + t m , n ′ ( q ) [ m ] q [ n ] q for all m and n . This paper gives a complete classification of quadratic addition rules, and also considers sequences of polynomials F = { f n ( q ) } n = 1 ∞ that satisfy the associated functional equation f m + n ( q ) = r n ′ ( q ) f m ( q ) + s m ′ ( q ) f n ( q ) + t m , n ′ f m ( q ) f n ( q ) . |
| Starting Page | 1 |
| Ending Page | 13 |
| Page Count | 13 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.jnt.2005.04.015 |
| Volume Number | 117 |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0503177v1.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/math/0503177v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math.NT/0503177.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/j.jnt.2005.04.015 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
