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AN EQUIVALENCE RELATION ARISING FROM MULTIPLICATION OF QUANTUM INTEGERS
Keywords:
quantum integer, generalized quantum integer, q-series, sumset, polynomial functional equation, cyclotomic polynomialDOI:
https://doi.org/10.17654/0972555524031Abstract
In the paper [5], we conjecture that the relation arising from multiplication of quantum integers and the problem of finding a set of criteria for extending the support bases of solutions of a functional equation arising from multiplication of quantum integers, which is described by Nathanson in [2] as Problem 3, is an equivalence relation. We show in [5] that the answer is affirmative in the case where the fields of coefficients of these solutions are $\mathbb{Q}$. In this paper, we prove that the answer is in fact also affirmative for all fields of characteristic zero. As a consequence of this result, we explain how it simplifies in several important ways the criteria for extension of support bases of solutions of the above functional equation.
Received: November 28, 2023
Accepted: February 6, 2024
References
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