THE REPRESENTATION OF INTEGERS BY QUADRATIC FORMS

Spring 2011 Everett Pitcher Lectures

MANJUL BHARGAVA
Professor of Mathematics
Princeton University        

Monday, March 14, 2011
THE REPRESENTATION OF INTEGERS BY QUADRATIC FORMS
Lewis Lab 270 - 7:00pm Lobby reception at 6:30pm
The classical Four squares theorem of Lagrange asserts that any positive integer can be expressed as the sum of four squares; that is, the quadratic form a2+b2+c2+d2 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 will show how all these questions turn out to have very simple and surprising answers.