The Eighth Power Moments of $\Delta(x)$

TL;DR

This paper derives an asymptotic formula for the eighth power moments of the error term in the divisor problem, using Voronoi's truncated formula involving Bessel functions, with a precise error estimate.

Contribution

It provides a new asymptotic formula for the eighth power moments of elta(x) with an improved error term, utilizing Voronoi's truncated formula.

Findings

Asymptotic formula for eighth power moments of elta(x)

Error term of order O(X^{3 - 1/254 + \u03b5})

Application of Voronoi's truncated formula involving Bessel functions

Abstract

Using Voronoi's truncated formula for $\Delta(x)$ involving Bessel functions, the first author derives an asymptotic formula for the eighth-power moments with an error term of order $O\left(X^{3 - \frac{1}{254} + \varepsilon}\right)$