Golden lattices

Abstract

Let $\vartheta :=\frac{-1+\sqrt{5}}{2}$ be the golden ratio. A golden lattice is an even unimodular $\mathbb{Z}[\vartheta ]$-lattice of which the Hilbert theta series is an extremal Hilbert modular form. We construct golden lattices from extremal even unimodular lattices and obtain families of dense modular lattices.