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Co-Poisson intertwining. (Entrelacement de co-Poisson.) (French. English summary) Zbl 1177.11074
Summary: The intimate link relating the functional equations of \(L\)-functions to the summatory formulas whose prototype is the Poisson formula is a familiar fact. This link involves the Fourier integral transform and its generalizations. Here, we shall reexamine the harmonic (as well as Hilbertian and distributional) meaning of the functional equations with the simplest shape, the one applying to the Riemann zeta function and to the Dirichlet \(L\)-series (many of our considerations have a more general range.) Certain formulas, related to but distinct from the Poisson-type formulas, play the central role. We call them co-Poisson formulas.

MSC:
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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