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

Canadian mathematical bulletin

A. Yehudayoff¹  A. Wigderson¹  P. Hrubeš¹ 

[1] School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA

关键词: composition formulas;    sums of squares;    Radon-Hurwitz number;   

DOI  :  10.4153/CMB-2011-143-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $sigma_{mathbb Z}(k)$ be the smallest $n$ such that there exists anidentity[(x_1^2 + x_2^2 + cdots + x_k^2) cdot (y_1^2 + y_2^2 + cdots + y_k^2)= f_1^2 + f_2^2 + cdots + f_n^2,] with $f_1,dots,f_n$ being polynomials with integer coefficients inthe variables $x_1,dots,x_k$ and $y_1,dots,y_k$. We prove that$sigma_{mathbb Z}(k) geq Omega(k^{6/5})$.

【 授权许可】

Unknown