Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 064, 6 pages      arXiv:1705.04913      https://doi.org/10.3842/SIGMA.2017.064

A Generalization of the Doubling Construction for Sums of Squares Identities

Chi Zhang a and Hua-Lin Huang b
a) School of Mathematics, Shandong University, Jinan 250100, China
b) School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

Received May 16, 2017, in final form August 13, 2017; Published online August 16, 2017

Abstract
The doubling construction is a fast and important way to generate new solutions to the Hurwitz problem on sums of squares identities from any known ones. In this short note, we generalize the doubling construction and obtain from any given admissible triple $[r,s,n]$ a series of new ones $[r+\rho(2^{m-1}),2^ms,2^mn]$ for all positive integer $m$, where $\rho$ is the Hurwitz-Radon function.

Key words: Hurwitz problem; square identity.

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