A functional equation originating from elliptic curves. (English) Zbl 1146.39037

Summary: We obtain the general solution and the stability of the functional equation
\[ \begin{split} f(x+y+z,u+v+w)+f(x+y - z,u+v+w)+2f(x,u - w)+2f(y,v - w) = \\ f(x+y,u+w)+f(x+y,v+w)+f(x+z,u+w)+ \\ +f(x - z,u+v - w)+f(y+z,v+w)+f(y-z,u+v-w).\end{split} \]
The function \(f(x,y)=x^{3}+ax+b - y^{2}\) having level curves as elliptic curves is a solution of the above functional equation.


39B32 Functional equations for complex functions
14H52 Elliptic curves
11G05 Elliptic curves over global fields
39B82 Stability, separation, extension, and related topics for functional equations
Full Text: DOI EuDML


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