TY - JOUR
T1 - Linearly dependent powers of binary quadratic forms
AU - Reznick, Bruce
N1 - Publisher Copyright:
© 2019 Mathematical Sciences Publishers.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Polynomial identities
KW - Super-Fermat problem for forms
UR - http://www.scopus.com/inward/record.url?scp=85079269570&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85079269570&partnerID=8YFLogxK
U2 - 10.2140/pjm.2019.303.729
DO - 10.2140/pjm.2019.303.729
M3 - Article
AN - SCOPUS:85079269570
SN - 0030-8730
VL - 303
SP - 729
EP - 755
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
IS - 2
ER -