<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we classify all solutions with cyclic and semi-cyclic semigroup supports of the functional equations arising from multiplication of quantum integers with fields of coefficients of characteristic zero. This also solves completely the classification problem proposed by Melvyn Nathanson and Yang Wang concerning the solutions, with semigroup supports which are not prime subsemigroups of ℕ, to these functional equations for the case of rational field of coefficients. As a consequence, we obtain some results for other problems raised by Nathanson concerning maximal solutions and extension of supports of solutions to these functional equations in the case where the semigroup supports are not prime subsemigroups of ℕ.</p>
</abstract>

In this paper, we classify all solutions with cyclic and semi-cyclic semigroup supports of the functional equations arising from multiplication of quantum integers with fields of coefficients of characteristic zero. This also solves completely the classification problem proposed by Melvyn Nathanson and Yang Wang concerning the solutions, with semigroup supports which are not prime subsemigroups of ℕ, to these functional equations for the case of rational field of coefficients. As a consequence, we obtain some results for other problems raised by Nathanson concerning maximal solutions and extension of supports of solutions to these functional equations in the case where the semigroup supports are not prime subsemigroups of ℕ.

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

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this paper, we classify all solutions with cyclic and semi-cyclic semigroup supports of the functional equations arising from multiplication of quantum...

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

Published Online: Oct 30, 2021

Page range: 1 - 40

Received: Aug 03, 2020

Accepted: Dec 26, 2020

DOI: https://doi.org/10.2478/udt-2021-0001

Keywords
quantum integer, quantum algebra, -series, semigroup, polynomial functional equation, cyclotomy

© 2021 Lan Nguyen et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Oct 30, 2021

Page range: 1 - 40

Received: Aug 03, 2020

Accepted: Dec 26, 2020

DOI: https://doi.org/10.2478/udt-2021-0001

Keywordsquantum integer, quantum algebra, -series, semigroup, polynomial functional equation, cyclotomy

© 2021 Lan Nguyen et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
quantum integer, quantum algebra, -series, semigroup, polynomial functional equation, cyclotomy