Date of Award

5-1-2015

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Earnest, Andrew

Second Advisor

Pericak-Spector, Kathleen

Abstract

For definite quadratic lattices over the rings of integers of algebraic number fields, it is shown that lattices are determined up to isometry by their local structure and sublattices of codimension 1. In particular, a theorem of Yoshiyuki Kitaoka for $\mathbb{Z}$-lattices is generalized to definite lattices over algebraic number fields.

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