## Number Theory - Siddhi Pathak (Queen's University)

### Tuesday, October 2nd, 2018

**Time:** 10:00 a.m. **Place:** Jeffery Hall 422

**Speaker:** Siddhi Pathak (Queen's University)

**Title:** On the values of the Epstein zeta function.

**Abstract:** Given a positive definite binary quadratic form, $Q(X,Y)$, the Epstein zeta function attached to $Q$ is given by $Z_Q(s) = \sum_{m,n} Q(m,n)^{-s}$, where the sum is over all tuples $(m,n)$ in $\mathbb{Z} \times \mathbb{Z}$, excluding $(0,0)$. This series converges absolutely for $Re(s)>1$. In this talk, we will present a result by J. R. Smart that 'evaluates' $Z_Q(k)$ for positive integers $k > 1$.