Graduate Student Colloquium

Ertan Elma, Department of Pure Mathematics, University of Waterloo

"The Pólya-Vinogradov Inequality"

Let p be a prime number. An integer which is not divisible by p is said to be a ''quadratic residue modulo p'' if it is congruent to a square modulo p. For example, 2 is a quadratic residue modulo 7 since 2 is congruent to 16 modulo 7.  In this talk, we will prove a 100-year-old inequality due to Pólya and Vinogradov independently and by using this, we will obtain an upper bound (in terms of p) for the least natural number which is ''not'' a quadratic residue modulo p.

MC 5501