科研之友
微信
新浪微博
Facebook
分享链接
摘要
Let R be a ring, F be a field and K subset of R an integral domain. In this paper we investigate general solutions f : K-2 -> R+ of the functional equations f(ux - vy, uy + vx) = f(x, y) f(u, v), f(ux + vy, uy - vx) = f(x, y) f(u, v) for all x, y is an element of K, and general solutions f : R-2 -> R+ of the functional equations f(ux + vy, uy + vx) = f(x, y) f(u, v), f(ux - vy, uy - vx) = f(x, y) f(u, v) for all x, y is an element of R. The above functional equations arise from number theory and are connected with the characterizations of the determinant and permanent of two-by-two matrices.
- 出版日期2016-4
