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• # Artykuł - szczegóły

## Open Mathematics

2005 | 3 | 2 | 203-214

## On the riemann zeta-function and the divisor problem II

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### Abstrakty

EN
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 $$\left| {\zeta \left( {\frac{1}{2} + it} \right)} \right|$$ . If E *(t)=E(t)-2πΔ*(t/2π) with $$\Delta *\left( x \right) + 2\Delta \left( {2x} \right) - \frac{1}{2}\Delta \left( {4x} \right)$$ , then we obtain $$\int_0^T {\left| {E*\left( t \right)} \right|^5 dt} \ll _\varepsilon T^{2 + \varepsilon }$$ and $$\int_0^T {\left| {E*\left( t \right)} \right|^{\frac{{544}}{{75}}} dt} \ll _\varepsilon T^{\frac{{601}}{{225}} + \varepsilon } .$$ It is also shown how bounds for moments of | E *(t)| lead to bounds for moments of $$\left| {\zeta \left( {\frac{1}{2} + it} \right)} \right|$$ .

EN

203-214

wydano
2005-06-01
online
2005-06-01

autor

### Bibliografia

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• [8] A. Ivić: “On the Riemann zeta-function and the divisor problem”, Central European J. Math., Vol. 2 (4), (2004), pp. 1–15.
• [9] A. Ivić and P. Sargos: “On the higher moments of the error term in the divisor problem”, to appear.
• [10] M. Jutila: “Riemann's zeta-function and the divisor problem”, Arkiv Mat., Vol. 21, (1983), pp. 75–96; “Riemann's zeta-function and the divisor problem II”, Arkiv Mat., Vol. 31, (1993), pp. 61–70. http://dx.doi.org/10.1007/BF02384301
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