Lenstra's Constant and Extreme Forms in Number Fields

Abstract

In this paper we compute γK,2 for K = ℚ(ρ), where ρ is the real root of the polynomial x ³ - x ² + 1 = 0. We refine some techniques introduced in [Baeza et al. 01] to construct all possible sets of minimal vectors for perfect forms. These refinements include a relation between minimal vectors and the Lenstra constant. This construction gives rise to results that can be applied in several other cases.

Keywords:

• 11H55
• Humbert forms
• extreme forms