Displaying similar documents to “Power mean-values for Dirichlet's polynomials and the Riemann zeta-function, II”

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.