On symmetries of roots of rational functions and the classification of rational function solutions of functional equations arising from multiplication of quantum integers with prime semigroup supports

On the Classification of Solutions of Quantum Functional Equations with Cyclic and Semi-Cyclic Supports

“…The results of this paper and those of [9] are also used in [12] to resolve another problem in this area concerning extensions of supports, not necessarily prime subsemigroups of N, of polynomial solutions with fields of coefficients K of characteristic zero. Moreover, we plan to establish in a future paper the analogues of the results in [9] for the rational function solutions with non-prime semigroup supports and fields of coefficients of characteristic zero (see [10,11] for the existence and characterization of rational function solutions with prime semigroup supports and fields of coefficients of characteristic zero).…”