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Twisted Dirichlet series and distributions. (English) Zbl 0704.11051

The purpose of this paper is to give a far-reaching generalization of Hamburger’s theorem which characterizes the Riemann zeta-function through its analytic properties (Dirichlet series expansion, analytic continuation and functional equation). In this paper the context is that of Dirichlet series associated with the S-integers in a global field F. The proof relies on establishing a “summation formula” and then exploiting this. The authors then make use of this to give an analytic criterion which decides whether a family of quasicharacters \((\mu_ v)\) defined on \(F_ V^{\times}\) for almost all places v of F consists of the components of a Größencharakter.
Reviewer: S.J.Patterson

MSC:

11R42 Zeta functions and \(L\)-functions of number fields
11M41 Other Dirichlet series and zeta functions
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References:

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