Displaying similar documents to “Bounds for double zeta-functions”

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 .

Zeta functions for the Riemann zeros

André Voros (2003)

Annales de l’institut Fourier

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A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structures, plus countably many special values) are explicitly displayed.

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...

On mean values of some zeta-functions in the critical strip

Aleksandar Ivić (2003)

Journal de théorie des nombres de Bordeaux

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For a fixed integer k ≥ 3 , and fixed 1 2 < σ < 1 we consider ∫ 1 T ζ ( σ + i t ) 2 k d t = ∑ n = 1 ∞ d k 2 ( n ) n - 2 σ T + R ( k , σ ; T ) , where R ( k , σ ; T ) = 0 ( T ) ( T → ∞ ) is the error term in the above asymptotic formula. Hitherto the sharpest bounds for R ( k , σ ; T ) are derived in the range min ( β k , σ k * ) < σ < 1 . We also obtain new mean value results for the zeta-function of holomorphic cusp forms and the Rankin-Selberg series.