1. bookVolumen 16 (2021): Edición 1 (June 2021)
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eISSN
2309-5377
Primera edición
30 Dec 2013
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2 veces al año
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On the Classification of Solutions of Quantum Functional Equations with Cyclic and Semi-Cyclic Supports

Publicado en línea: 30 Oct 2021
Volumen & Edición: Volumen 16 (2021) - Edición 1 (June 2021)
Páginas: 1 - 40
Recibido: 03 Aug 2020
Aceptado: 26 Dec 2020
Detalles de la revista
License
Formato
Revista
eISSN
2309-5377
Primera edición
30 Dec 2013
Calendario de la edición
2 veces al año
Idiomas
Inglés
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.

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[1] CHEREDNIK, I.: On q-analogues of Riemann’s zeta, Selecta Math. N S. 7 (2001), 447–491.10.1007/s00029-001-8095-6 Search in Google Scholar

[2] KOBLITZ, N.: On Carlitz’s q-Bernoulli numbers, J. Number Theory 14 (1982), 332–339.10.1016/0022-314X(82)90068-3 Search in Google Scholar

[3] MOAK, D. S.: The q-analogue of sterling formula, Rocky Mountain J. Math. 14 (1984), 403–413.10.1216/RMJ-1984-14-2-403 Search in Google Scholar

[4] NATHANSON, M. B.: A functional equation arising from multiplication of quantum integers, J. Number Theory 103 (2003), no. 2, 214–233. Search in Google Scholar

[5] NATHANSON, M. B.: Formal power series arising from multiplication of quantum integers, Unusual applications of number theory DIMACs Ser. Discrete Math. Theoret. Comput. Sci. Vol. 64, (2004) Amer. Math. Soc., Providence, RI, pp.145–157. Search in Google Scholar

[6] NATHANSON, M. B.: Linear quantum addition rules, Integers 7 (2007), no. 2, 1–6 (A 27). Search in Google Scholar

[7] NGUYEN, L.: On the solutions of a functional equation arising from multiplication of quantum integers, J. Number Theory 130 (2010), no. 6, 1292–1347. Search in Google Scholar

[8] NGUYEN, L.: On the classification of solutions of a functional equation arising from multiplication of quantum integers, Unif. Distrib. Theory 8 (2013), no. 2, 49–120. Search in Google Scholar

[9] NGUYEN, L.: Nathanson quantum functional equations and the non-prime semi-group support polynomial solutions, Semigroup Forum 93 (2016) no. 3, 459–490. Search in Google Scholar

[10] NGUYEN, L.: 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, Aequationes Math. 92 (2018), 1001–1035, DOI:10.1007/s00010-018-0607-y.10.1007/s00010-018-0607-y Search in Google Scholar

[11] NGUYEN, L.: On the rational function solutions of functional equations arising from multiplication of quantum integers, 293 Math. Z. (2019), 903–933, DOI:10.1007/s00209-019-02380-z.10.1007/s00209-019-02380-z Search in Google Scholar

[12] NGUYEN, L.: Quantum functional equations and extension of non-prime supports for solutions with field of coefficients ℚ, (preprint). Search in Google Scholar

[13] SATOH, J.: q-analogue of Riemann’s ζ-function and q-Euler numbers, J. Number Theory 31 (1989), 346–362.10.1016/0022-314X(89)90078-4 Search in Google Scholar

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