English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We express the Riemann zeta function $\zeta\left(s\right)$ of argument$s=\sigma+i\tau$ with imaginary part $\tau$ in terms of three absolutelyconvergent series. The resulting simple algorithm allows to compute, toarbitrary precision, $\zeta\left(s\right)$ and its derivatives using at most$C\left(\epsilon\right)\left|\tau\right|^{\frac{1}{2}+\epsilon}$ summands forany $\epsilon>0$, with explicit error bounds. It can be regarded as aquantitative version of the approximate functional equation. The numericalimplementation is straightforward. The approach works for any type of zetafunction with a similar functional equation such as Dirichlet $L$-functions, orthe Davenport-Heilbronn type zeta functions.

The Zetafast algorithm for computing zeta functions