Lecture Details
Name: Manuel Maestre (Universidad de Valencia)Speaking: Fri 10th May 14:30 - 14:55Title: Universal Dirichlet seriesAbstract: The purpose of this talk is to show the existence of a Dirichlet series $\sum_{n=1}^\infty\frac{a_n}{n^s}$ such that $\sum_{n=1}^\infty\frac{|a_n|}{n^\sigma}$ is convergent for every $\sigma>0$ and satisfying the following ``universal property":
Given $K\subset \{z\in \mathbb{C} :\text{Re}\, z\leq 0\}$ a compact set with connected complement and given $g:K\to \mathbb{C}$ a function continuous function on $K$ and holomorphic on its interior, there exists a subsequence $(S_{N_j})$ of $S_N=\sum_{n=1}^N\frac{a_n}{n^s}$ such that $(S_{N_j})$ converges uniformly to $g$ on $K$.
This is a joint work with R.M. Aron, F. Bayart, P. Gauthier and V. Nestoridis.