On the riemann zeta-function and the divisor problem II

Aleksandar Ivić

Open Mathematics, Tome 3 (2005), p. 203-214 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $|ζ (\frac{1}{2} + i t)|$ . If E *(t)=E(t)-2πΔ*(t/2π) with $Δ * (x) + 2 Δ (2 x) - \frac{1}{2} Δ (4 x)$ , then we obtain $\int_{0}^{T} {|E * (t)|}^{5} d t ≪_{ε} T^{2 + ε}$ and $\int_{0}^{T} {|E * (t)|}^{\frac{544}{75}} d t ≪_{ε} T^{\frac{601}{225} + ε} .$ It is also shown how bounds for moments of | E *(t)| lead to bounds for moments of $|ζ (\frac{1}{2} + i t)|$ .

Publié le : 2005-01-01

Zbl 1132.11343

EUDML-ID : urn:eudml:doc:268775

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     author = {Aleksandar Ivi\'c},
     title = {On the riemann zeta-function and the divisor problem II},
     journal = {Open Mathematics},
     volume = {3},
     year = {2005},
     pages = {203-214},
     zbl = {1132.11343},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02479196}
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Aleksandar Ivić. On the riemann zeta-function and the divisor problem II. Open Mathematics, Tome 3 (2005) pp. 203-214. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02479196/

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