English

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

Number Theory 2025-07-29 v1

Abstract

Using Voronoi's truncated formula for Δ(x)\Delta(x) involving Bessel functions, the first author derives an asymptotic formula for the eighth-power moments with an error term of order O(X31254+ε)O\left(X^{3 - \frac{1}{254} + \varepsilon}\right)

Keywords

Cite

@article{arxiv.2507.19528,
  title  = {The Eighth Power Moments of $\Delta(x)$},
  author = {Junhao Liao and Junjie Liao},
  journal= {arXiv preprint arXiv:2507.19528},
  year   = {2025}
}