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Ertan Elma, Department of Pure Mathematics, University of Waterloo

"Discrete Mean Values of Dirichlet L-functions"

Let χ be a Dirichlet character modulo a prime number p ⩾ 3 and let \mathfrak a_χ:=(1-χ(-1))/2. Define the mean value
\begin{align*}
\mathcal{M}_{p}(s,\chi):=\frac{2}{p-1}\sum_{\substack{\psi \bmod p\\\psi(-1)=-1}}L(1,\psi)L(s,\chi\overline{\psi})
\end{align*}
for a complex number s such that s≠ 1 if \mathfrak a _χ=1.

Brett Nasserden, Department of Pure Mathematics, University of Waterloo

"Normal forms of dominant polynomial morphisms of the affine plane"