# Ramanujan Graphs (VI)

#### by Sanming Zhou

Institution: The University of Melbourne
Date: Wed 13th March 2013
Time: 11:00 AM
Location: Room 107, Richard Berry

Abstract: We will continue our discussion on some basic definitions and results in number theory, which will be used later in the construction of the expander graphs $X^{p, q}$ of Lubotzky, Phillips and Sarnak. Topics to be discussed this week include: Legendre's formula for $r_2(n)$, the law of quadratic reciprocity, Jacobi's formula for $r_4(n)$, quaternions, and the arithmetic of integer quaternions.