Quadratic addition rules for quantum integers |
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Authors: | Alex V Kontorovich |
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Institution: | a Department of Mathematics, Columbia University, New York, NY 10027, USA b Department of Mathematics, Lehman College (CUNY), Bronx, NY 10468, USA |
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Abstract: | For every positive integer n, the quantum integer n]q is the polynomial n]q=1+q+q2+?+qn-1. A quadratic addition rule for quantum integers consists of sequences of polynomials , , and such that for all m and n. This paper gives a complete classification of quadratic addition rules, and also considers sequences of polynomials that satisfy the associated functional equation . |
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Keywords: | primary 30B12 81R50 secondary 11B13 |
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