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

abstract

• 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.

authors

• Sottile, Frank

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

publisher

• Elsevier  Publisher

published in

• Comptes Rendus Mathematique (Academie des Sciences)  Journal

Digital Object Identifier (DOI)

• 10.1016/j.crma.2004.09.014

start page

• 617

end page

• 620

volume

• 339

issue

• 9

URL

• http://dx.doi.org/10.1016/j.crma.2004.09.014