QUANTUM FUNCTIONAL EQUATIONS AND EXTENSION OF NON-PRIME SUPPORTS FOR SOLUTIONS WITH RATIONAL FIELD OF COEFFICIENTS

In this paper, we provide a solution to a problem raised by Melvyn Nathanson, concerning the extensions of supports for solutions of functional equations arising from quantum arithmetic, in the case where the supports of these solutions are not necessarily prime semigroups and their field of coefficients is Q. Contrary to the prime semigroup support case, a solution in this case requires a different approach due to the lack of prime indexed elements.