Linearly dependent powers of binary quadratic forms

Research output: Contribution to journalArticlepeer-review


Given an integer d ≥ 2, what is the smallest r so that there is a set of binary quadratic formsg (f1,...,fr) for which (fdj) is nontrivially linearly dependent? We show that ifr ≤4, then d ≤5, and for d ≥ 4, construct such a set with r =d/2+2. Many explicit examples are given, along with techniques for producing others.

Original languageEnglish (US)
Pages (from-to)729-755
Number of pages27
JournalPacific Journal of Mathematics
Issue number2
StatePublished - 2019


  • Polynomial identities
  • Super-Fermat problem for forms

ASJC Scopus subject areas

  • General Mathematics


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