Zeta

• The Riemann Zeta function is \( \zeta(z)=\sum_{n=1}^{\inf}\frac{1}{n^z} \)
• An old problem is to show that the non-trivial zeroes of the \( \zeta(z) \) function lie on the critical line \( z=0.5+yi \).
• Presented is an interactive web page for the exploration of the zeta function.
• This compiled document is at http://rpubs.com/dlarue/zetapres.
• The source for this document the Shiny application, is at https://github.com/David-Maurice-Larue/zeta.
• The interactive Shiny application, with documentation, is at https://david-maurice-larue.shinyapps.io/ShinyZetaPlot/.

We make use of the R library “pracma” to compute values of the zeta function.

library(pracma)
z=2+3i
zeta(z)

[1] 0.798022-0.1137443i