*Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam.*

Tuesday, September 1, 2015

2:10 p.m.

BA6183

PhD Candidate: Alex Dahl

Supervisor: Valentin Blomer

Thesis title: Subconvexity for a double Dirichlet series and non-vanishing of L-functions

********************

Abstract:

We study a double Dirichlet series of the form $ \sum_{d} L(s,\chi_d \chi)\chi'(d)d^{-w} $, where $\chi$and $\chi’$ are quadratic Dirichlet characters with prime conductors $N$ and $M$ respectively. A functional equation group isomorphic to the dihedral group of order 6 continues the function meromorphically to $\mathbb{C}^2$. A convexity bound at the central point is established to be $(MN)^{3/8+\varepsilon}$ and a subconvexity bound of $(MN(M+N))^{1/6+\varepsilon}$ is proven. This bound is used to prove an upper bound for the smallest positive integer $d$ such that $L(1/2,\chi_{dN})$ does not vanish.

A copy of the thesis can be found here: Alexander Dahl – Thesis

## no comment as of now