Sums of squares on hypersurfaces

Abstract

We show that the Pythagoras number of rings of type $\mathbb{R}[x,y,\sqrt{f(x,y)}]$ is infinite, provided that the polynomial $f(x,y)$ satisfies some mild conditions.

minor changes, final version, 9 pages

References in corpus (3)

• Positive semidefinite analytic functions on real analytic surfaces
• Gram Spectrahedra of Ternary Quartics
• Sums of even powers of k-regulous functions

Cited by in corpus (1)

• On Waring numbers of henselian rings