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Mean-periodicity and zeta functions

Ivan Fesenko, Guillaume Ricotta, Masatoshi Suzuki (2012)

Annales de l’institut Fourier

This paper establishes new bridges between zeta functions in number theory and modern harmonic analysis, namely between the class of complex functions, which contains the zeta functions of arithmetic schemes and closed with respect to product and quotient, and the class of mean-periodic functions in several spaces of functions on the real line. In particular, the meromorphic continuation and functional equation of the zeta function of an arithmetic scheme with its expected analytic shape is shown...

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