A functional equation related to the product in a quadratic number field

被引：7

作者：

Berrone, Lucio R. ^{[1
]}

Dieulefait, Luis V. ^{[2
]}

机构：

[1] Univ Nacl Rosario, CONICET, Fac Ciencias Exactas Ing & Agrim, Lab Acust & Electroacust, RA-2000 Rosario, Santa Fe, Argentina

[2] Univ Barcelona, Dept Algebra & Geometria, E-08007 Barcelona, Spain

来源：

AEQUATIONES MATHEMATICAE | 2011年 / 81卷 / 1-2期

关键词：

Functional equation; additive and multiplicative function; quadratic field;

D O I：

10.1007/s00010-010-0049-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The functional equation f(x1, y1) f(x2,y2) = f(x1x2 + alpha y1y2, x1y2 + x2y1), (x1, y1), (x2, y2) is an element of R(2) arises from the formula for the product of two numbers in the quadratic field Q(root alpha). the general solution f : R -> R to this equation is determined. Moreover, it is shown that no more general equations arise from a change of basis in the field.

引用

页码：167 / 175

页数：9