A computational algorithm for the Hardy function $Z(t)$, utilising sub-sequences of generalised cubic Gauss sums, with an overall operational complexity of $O((t/{\epsilon }_t{)}^{[.25,.3]}(\log t{)}^{2+o(1)})$, for $t\in [10^{23},10^{35}]$

David Lewis, Ashley Brereton

In 2011 G. A. Hiary devised a computational algorithm for the Hardy function $Z(t)$, requiring just $O(t^{1/3}(\log (t){)}^{\hat{I}}º)$ operations. This compares to $O(\sqrt{t})$ operations n…