An Asymptotic Bound on the Composition Number of Integer Sums of Squares Formulas

Abstract

AbstractLet σZ(k) be the smallest n such that there exists an identity , with f1, . . . , fn being polynomials with integer coefficients in the variables x1, . . . , xk and y1, . . . , yk. We prove that σℤ(k) ≥ (k6/5).