W. Zhai

most citedOn the mean square of the error term for the two-dimensional divisor problems(II)

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math.NT2008★ 1 cited

On the mean square of the error term for the two-dimensional divisor problems(II)

Xiaodong Cao, Wenguang Zhai

Let $Δ (a, b; x)$ denote the error term of the general two-dimensional divisor problem. In this paper we shall study the relation between the discrete mean value $\sum_{n\leq T}Δ^2(a,…

math.NT2008

On the mean square of the error term for the two-dimensional divisor problem (I)

Wenguang Zhai, Xiaodong Cao

Suppose $a$ and $b$ are two fixed positive integers such that $(a, b) = 1.$ In this paper we shall establish an asymptotic formula for the mean square of the error term $Δ_{a, b} (x)$ o…

math.NT2008

On the fourth power moment of $Δ (x)$ and $E (x)$ in short intervals

Yoshio Tanigawa, Wenguang Zhai

Let $Δ (x)$ and $E (x)$ be error terms of the sum of divisor function and the mean square of the Riemann zeta function, respectively. In this paper their fourth power moments for sho…

math.NT2008

On higher-power moments of $Δ (x)$ (III)

Wenguang Zhai

Let $Δ (x)$ be the error term of the Dirichlet divisor problem. An asymptotic formula with the error term $O (T^{53/28 + ε})$ is established for the integral $\int_{1}^{T} Δ^{4} (x) d x .$ Simila…

On the mean square of the error term for the two-dimensional divisor problems(II)

On the mean square of the error term for the two-dimensional divisor problem (I)

On the fourth power moment of Δ(x) and E(x) in short intervals

On higher-power moments of Δ(x)(III)

On the fourth power moment of $Δ (x)$ and $E (x)$ in short intervals

On higher-power moments of $Δ (x)$ (III)