## Departmental PhD Thesis Exam – Alexander Dahl

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

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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