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On general \(L\)-functions. (English) Zbl 0809.11046

From the introduction: “The aim of the present paper is to develop in a unified way some analytic results for a rather general class of \(L\)- functions. This class is defined axiomatically and the axioms are modelled on the basic properties of the zeta and \(L\)-functions associated with algebraic number fields and automorphic forms which appear in number theory. We concentrate our investigations mainly on problems connected with the zero-free regions and real zeros.”
This long paper contains several nice results, and many technicalities; therefore the reviewer prefers not to try to give a survey of results but only to state some keywords like functional equations, Rankin-Selberg type convolution, Aramata-Brauer theorem, Siegel-Brauer theorem.

MSC:

11M41 Other Dirichlet series and zeta functions
11R42 Zeta functions and \(L\)-functions of number fields
11F66 Langlands \(L\)-functions; one variable Dirichlet series and functional equations
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