Universal quadratic forms and indecomposables in numberfields: A survey

Abstract

We give an overview of universal quadratic forms and lattices, focusing onthe recent developments over the rings of integers in totally real number fields. Inparticular, we discuss indecomposable algebraic integers as one of the main tools.

Keywords

• Universal quadratic form
• quadratic lattice
• totally real number field
• indecomposable algebraic integer
• continued fraction