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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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