A new approach to Hilbert's theorem on ternary quartics Academic Article uri icon


  • Hilbert proved that a non-negative real quartic form f (x, y, z) is the sum of three squares of quadratic forms. We give a new proof which shows that if the plane curve Q defined by f is smooth, then f has exactly 8 such representations, up to equivalence. They correspond to those real 2-torsion points of the Jacobian of Q which are not represented by a conjugation-invariant divisor on Q. 2004 Acadmie des sciences. Published by Elsevier SAS. All rights reserved.

published proceedings

  • Comptes Rendus Mathmatique

altmetric score

  • 3

author list (cited authors)

  • Powers, V., Reznick, B., Scheiderer, C., & Sottile, F.

citation count

  • 16

complete list of authors

  • Powers, Victoria||Reznick, Bruce||Scheiderer, Claus||Sottile, Frank

publication date

  • January 2004