|Current Workshop | Overview||Back | Print | Home | Search ||
Lorentz Center Highlights
Manjul BhargavaPrinceton 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
Geomagic, Research Triangle Park, North Carolina