Displaying similar documents to “Zeta functions for idelic pseudo-measures”

Idele characters in spectral synthesis on 𝐑 / 2 π 𝐙

John J. Benedetto (1973)

Annales de l'institut Fourier

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Let s ∈ C , x ∈ R / 2 π Z . We construct Dirichlet series F ( x , x ) where for each fixed s in a half plane, Re F ( x , x ) , as a function of x , is a non-synthesizable absolutely convergent Fourier series. Because of the way the frequencies in F are chosen, we are motivated to introduce a class of synthesizable absolutely convergent Fourier series which are defined in terms of idele characters. We solve the “problem of analytic continuation” in this setting by constructing pseudo-measures, determined by idele characters, when...

Bounds for double zeta-functions

Isao Kiuchi, Yoshio Tanigawa (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this paper we shall derive the order of magnitude for the double zeta-functionof Euler-Zagier type in the region 0 ≤ ℜ s j < 1 ( j = 1 , 2 ) .First we prepare the Euler-Maclaurinsummation formula in a suitable form for our purpose, and then we apply the theory of doubleexponential sums of van der Corput’s type.

Some problems on mean values of the Riemann zeta-function

Aleksandar Ivić (1996)

Journal de théorie des nombres de Bordeaux

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Several problems and results on mean values of ζ ( s ) are discussed. These include mean values of | ζ ( 1 2 + i t ) | and the fourth moment of | ζ ( σ + i t ) | for 1 / 2 < σ < 1 .