Displaying similar documents to “Mean values connected with the Dedekind zeta-function of a non-normal cubic field”

On the riemann zeta-function and the divisor problem II

Aleksandar Ivić (2005)

Open Mathematics

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Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of ζ 1 2 + i t . If E *(t)=E(t)-2πΔ*(t/2π) with Δ * x + 2 Δ 2 x - 1 2 Δ 4 x , then we obtain ∫ 0 T E * t 5 d t ≪ ε T 2 + ε and ∫ 0 T E * t 544 75 d t ≪ ε T 601 225 + ε . It is also shown how bounds for moments of | E *(t)| lead to bounds for moments of ζ 1 2 + i t .

Integral Representations of the Logarithmic Derivative of the Selberg Zeta Function

Gušić, Dženan (2010)

Mathematica Balkanica New Series

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AMS Subj. Classification: MSC2010: 11F72, 11M36, 58J37 We point out the importance of the integral representations of the logarithmic derivative of the Selberg zeta function valid up to the critical line, i.e. in the region that includes the right half of the critical strip, where the Euler product definition of the Selberg zeta function does not hold. Most recent applications to the behavior of the Selberg zeta functions associated to a degenerating sequence of finite volume,...

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.