zetaRS approximates Riemann's zeta(0.5 + i*t) for large t

版本 1.2.0 (7.7 KB) 作者: Thomas

Fast computation of Riemann's zeta function on the critical strip using the Riemann Siegel formula.

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更新时间 2020/12/9

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Run for example "zetaRS(100000)" to obtain an approximate value of zeta(0.5 + i*100000).
For large t, the routine is much faster than the zeta function that comes with Matlab's symbolic toolbox. The error is very small for large t, but zetaRS is not very precise for small t.
Example: >> tic; zetaRS(10000000), toc
ans = 11.4580 - 8.6434i
Elapsed time is 0.009604 seconds.
>> tic; zeta(0.5+10000000i), toc
ans = 11.4580 - 8.6434i
Elapsed time is 175.978625 seconds.
Source is: Xavier Gourdon and Pascal Sebah: Numerical evaluation of the Riemann Zeta-function, Numbers, constants and computation ,
or: http://numbers.computation.free.fr/Constants/Miscellaneous/zetaevaluations.pdf

引用格式

Thomas (2024). zetaRS approximates Riemann's zeta(0.5 + i*t) for large t (https://www.mathworks.com/matlabcentral/fileexchange/83278-zetars-approximates-riemann-s-zeta-0-5-i-t-for-large-t), MATLAB Central File Exchange. 检索来源 2024/7/22.