Displaying similar documents to “Zeta functions for the Riemann zeros”

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 .

Riemann's Hypothesis

Rusev, Peter (2010)

Union of Bulgarian Mathematicians

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Riemann’s memoir is devoted to the function π(x) defined as the number of prime numbers less or equal to the real and positive number x. This is really the fact, but the “main role” in it is played by the already mentioned zeta-function.

New integral representations for the square of the Riemann zeta-function

Andreas Guthmann (1997)

Acta Arithmetica

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Introduction. The recent discovery of an analogue of the Riemann-Siegel integral formula for Dirichlet series associated with cusp forms [2] naturally raises the question whether similar formulas might exist for other types of zeta functions. The proof of these formulas depends on the functional equation for the underlying Dirichlet series. In both cases, for ζ(s) and for the cusp form zeta functions, only a simple gamma factor is involved. The next simplest case arises when two such...