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Results tagged with dirichlet-series
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user 37555
8
votes
meromorphic extension of dirichlet series
The maximal domain of meromorphic continuation of a Dirichlet series can be anything.
More precisely, for every connected open subset $O$ of $\mathbb{C}$, which contains the half plane $\{\Re s>1\}$, …
4
votes
Real non trivial zeros of Dirichlet L-functions
The non-vanishing of $L$-series on the real line received a lot of attention, unfortunately, there is still a lot we do not know, even in the non-quadratic case. This circle of problems even has its o …
6
votes
What is the relationship between the abscissa of holomorphy and abscissa of convergence of a...
In general the answer is no, but if you assume that the $a_n$ are non-negative, then Landau's theorem tells you that $\phi$ has a singularity at $\sigma_{\mathrm{conv}}$, in particular $\sigma_{\mathr …
2
votes
Modern Algebraic Geometry and Analytic Number Theory
From the point of view of analytic number theory the most important specific result which is proved using algebraic geometry is Burgess' bounds for character sums. The proof relies on Wiles bound for …