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

[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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