Date: Jan 21, 2013 12:23 AM
Author: David Bernier
Subject: PARI/gp wins my Riemann zeta speed contest, so far

I had done my own Riemann zeta computations with Bernoulli numbers,
computing in days a few 10,000 (say 55,000) decimals of
the imaginary part of the first non-trivial zero
1/2 + i*14.13... using PARI-gp.

This time, I used PARI-gp's own zeta(.):

? system(date);zeta(t);system(date)
Sun Jan 20 03:36:28 EST 2013
Sun Jan 20 07:10:17 EST 2013


// 20,000 decimals precision
// t is with 1/10^400 of first non-trivial zero.

3 hours and 34 minutes for 20017 significant digits
near 1/2 + i*14.134725141734693790457251983562470270784257



? \p
realprecision = 20017 significant digits (20000 digits displayed)
? a=zeta(t);

? ?
Help topics: for a list of relevant subtopics, type ?n for n in
0: user-defined functions (aliases, installed and user functions)
1: Standard monadic or dyadic OPERATORS
2: CONVERSIONS and similar elementary functions
3: TRANSCENDENTAL functions
4: NUMBER THEORETICAL functions
5: Functions related to ELLIPTIC CURVES
6: Functions related to general NUMBER FIELDS

12: The PARI community

Also:
=====================

On PARI-gp, I'm trying to get the readline library included.
That means backspace reprints the previous query, etc.

David Bernier