Lorentz Center - Lorentz Center Highlights
  Current Workshop  |   Overview   Back  |   Print   |   Home   |   Search   |     

    Lorentz Center Highlights

Manjul Bhargava

Princeton University, USA

Sums of squares and the "290-Theorem"

ABSTRACT: The famous "Four Squares Theorem" of Lagrange asserts that any positive integer can be expressed as the sum of four square numbers. That is, the quadratic form a^2 + b^2 + c^2 + d^2 "represents" all (positive) integers.

When does a general quadratic form represent all integers? When does it represent all odd integers? When does it represent all primes? We show how all these questions turn out to have very simple and surprising answers. Geomagic, Research Triangle Park, North Carolina