An asymptotic bound on the composition number of integer sums of squares formulas

P. Hrubes*, A. Wigderson, A. Yehudayoff

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let Z(k) be the smallest n such that there exists an identity (x 2 + x22 + . . . + x2k ).(y21 + y22 + . . . + y 2k ) = f21 + f2 2 + . . . + f2n , with f1, . . . , fn being polynomials with integer coefficients in the variables x1, . . . , xk and y1, . . . , yk. We prove that Z(k) ≥(k6/5).

Original languageEnglish
Pages (from-to)70-79
Number of pages10
JournalCanadian Mathematical Bulletin
Volume56
Issue number1
DOIs
StatePublished - 2013
Externally publishedYes

Keywords

  • Composition formulas
  • Radon-Hurwitz number
  • Sums of squares

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