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