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PARI/gp wins my Riemann zeta speed contest, so far
Posted:
Jan 21, 2013 12:23 AM


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 nontrivial zero 1/2 + i*14.13... using PARIgp.
This time, I used PARIgp'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 nontrivial 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: userdefined 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 PARIgp, I'm trying to get the readline library included. That means backspace reprints the previous query, etc.
David Bernier



