The 290-Theorem and Representing Numbers by Quadratic Forms

  • Date: 10/11/2006

Jonathan Hanke (Duke University)


University of British Columbia


This talk will describe several finiteness theorems for quadratic
forms, and progress on the question: "Which positive definite
integer-valued quadratic forms represent all positive integers?". The
answer to this question depends on settling the related question "Which
integers are represented by a given quadratic form?" for finitely many
forms. The answer to this question can involve both arithmetic and
analytic techniques, though only recently has the analytic approach
become practical. We will describe the theory of quadratic forms as it
relates to answering these questions, its connections with the theory
of modular forms, and give an idea of how one can obtain explicit
bounds to describe which numbers are represented by a given quadratic

Other Information: 

Algebraic Geometry Seminar 2006