A parametric functional equation originating from number theory



Abstract

Let S be a semigroup and α,β∈ℝ. The purpose of this paper is to determine the general solution f:ℝ2→S of the following parametric functional equation
f(x1x2+αy1y2,x1y2+x2y1+βy1y2) = f(x1,y1)f(x2,y2),
for all (x1,y1), (x2,y2)∈ℝ2, that generalizes some functional equations arising from number theory and is connected with the characterizations of the determinant of matrices.


Keywords

functional equation; number theory; character; multiplicative function; monoid; additive function

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Published : 2022-01-17


MouzounA., ZeglamiD., & AissiY. (2022). A parametric functional equation originating from number theory. Annales Mathematicae Silesianae, 36(1), 71-91. Retrieved from https://www.journals.us.edu.pl/index.php/AMSIL/article/view/13462

Aziz Mouzoun  mouzounposte@gmail.com
Department of Mathematics, E.N.S.A.M, Moulay ISMAÏL University, Morocco  Morocco
https://orcid.org/0000-0001-7966-0391
Driss Zeglami 
Department of Mathematics, E.N.S.A.M, Moulay ISMAÏL University, Morocco  Morocco
Youssef Aissi 
Department of Mathematics, E.N.S.A.M, Moulay ISMAÏL University, Morocco  Morocco



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