论文信息 - On hybrid moments of $$\Delta _2(x)$$ and $$\Delta _3(x)$$

On hybrid moments of $$\Delta _2(x)$$ and $$\Delta _3(x)$$

Let $$k\geqslant 2$$ be a fixed natural number and $$d_k(n)$$ denote the number of ways n can be written as a product of k positive integers. We use $$\Delta _k(x)$$ to denote the error term in the asymptotic formula of the summatory function of $$d_k(n).$$ The aim of this paper is to study the hybrid moments of $$\Delta _2(x)$$ and $$\Delta _3(x)$$ . The higher power moments of $$\Delta _2(x)$$ are also studied.

[1] A. Ivic,et al. Higher moments of the error term in the divisor problem , 2004, 0904.2271.

[2] D. R. Heath-Brown. The distribution and moments of the error term in the Dirichlet divisor problem Acta Arith , 1992 .

[3] Gareth Jones,et al. The Riemann Zeta-Function , 1992 .

[4] On the mean square formula of the error term in the Dirichlet divisor problem , 2009, Mathematical Proceedings of the Cambridge Philosophical Society.

[5] Y. Tanigawa,et al. Tong-type identity and the mean square of the error term for an extended Selberg class , 2015, 1501.04269.

[6] Jinjia Li. On the seventh power moment of Δ(x) , 2017 .

[7] H. Cramér. Über zwei Sätze des Herrn G. H. Hardy , 1922 .

[8] W. Zhai,et al. ON THE FIFTH-POWER MOMENT OF Δ(x) , 2011 .

[9] Jinjia Li. On the Seventh Power Moment of $\Delta(x)$ , 2016, 1601.05515.

[10] Higher-Power Moments of δ(x), E(t) and P(x) , 1992 .

[11] Olivier Robert,et al. Three-dimensional exponential sums with monomials , 2006 .

[12] W. Zhai. On higher-power moments of $\Delta(x)$(III) , 2008, 0805.1523.

[13] W. Zhai. N T ] 2 7 N ov 2 01 7 ON CERTAIN INTEGRALS INVOLVING THE DIRICHLET DIVISOR PROBLEM Aleksandar Ivić , 2018 .

[14] W. Zhai. On higher-power moments of $E(t)$ , 2004 .