Turing's method to compute zeta function

Question

I am trying to learn about Turing's method to perform calculations involving zeta function. I would like to learn the details of this method but the only references I found are his 1943 and 1953 papers on "The Turing Digital archive" but a lot of the details are left to the reader.

Are there any other books/literature where I can find a detailed introduction of Turing's methods for zeta function?

Answer 1

Turing's 1952 paper "Some calculations of the Riemann zeta-function" is presented by Cooper and van Leeuwen in their book "Alan Turing - His Work and Impact" with quite some details.

Some additional references :

• Edwards' "Riemann's Zeta function" book (page $172-175$ possibly inaccessible...)
• Hejhal and Odlyzko (2011) "Alan Turing and the Riemann Zeta Function"
• Trudgian's papers "Improvements to Turing's Method I" and II.

Answer 2

I found the explanation in Section 3.2 of http://numbers.computation.free.fr/Constants/Miscellaneous/zetazeros1e13-1e24.pdf quite helpful.

Also p172-175 of Riemann’s Zeta Function (H.M. Edwards) as stated by other user.