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 $E^{} (t) = E (t) - 2 π Δ^{} (t / 2 π)$ with $\Delta^*(x)

-\Delta(x) + 2\Delta(2x) - 1/2\Delta(4x) $a n d w e s e t$ \int_0^T E^(t),dt = 3\pi T/4 + R(T) $, t h e n w e o b t a i n$ $ \int_T^{T+H}(E^(t))^2,dt \gg HT^{1/3}\log^3T $a n d$ HT\log^3T \ll \int_T^{T+H}R^2(t),dt \ll HT\log^3T, $ $f o r$ T^{2/3+\epsilon}\le H \le T$.

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 $E^{} (t) = E (t) - 2 π Δ^{} (t / 2 π)$ with $\Delta^*(x)

On some mean square estimates for the zeta-function in short intervals

文献摘要

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 $E^{} (t) = E (t) - 2 π Δ^{} (t / 2 π)$ with $\Delta^*(x)

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On some mean square estimates for the zeta-function in short intervals

文献摘要

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 $E^{} (t) = E (t) - 2 π Δ^{} (t / 2 π)$ with $\Delta^*(x)

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On some mean square estimates for the zeta-function in short intervals

文献摘要

Let Δ(x)Δ(x) denote the error term in the Dirichlet divisor problem, and E(T)E(T) the error term in the asymptotic formula for the mean square of ∣ζ(1/2+it)∣∣ζ(1/2+it)∣. If E∗(t)=E(t)−2πΔ∗(t/2π)E∗(t)=E(t)−2πΔ∗(t/2π) with $\Delta^*(x)

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On some mean square estimates for the zeta-function in short intervals

文献摘要

Let Δ(x)Δ(x) denote the error term in the Dirichlet divisor problem, and E(T)E(T) the error term in the asymptotic formula for the mean square of ∣ζ(1/2+it)∣∣ζ(1/2+it)∣. If E∗(t)=E(t)−2πΔ∗(t/2π)E∗(t)=E(t)−2πΔ∗(t/2π) with $\Delta^*(x)

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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 $E^{} (t) = E (t) - 2 π Δ^{} (t / 2 π)$ with $\Delta^*(x)

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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 $E^{} (t) = E (t) - 2 π Δ^{} (t / 2 π)$ with $\Delta^*(x)

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