Re: Question on finding a Riemann Zeta function zero for high values of

Cohen Henri on Thu, 23 Oct 2025 11:38:46 +0200

Re: Question on finding a Riemann Zeta function zero for high values of s

To: "Bill Allombert" <Bill.Allombert@math.u-bordeaux.fr>
Subject: Re: Question on finding a Riemann Zeta function zero for high values of s
From: "Cohen Henri" <Henri.Cohen@math.u-bordeaux.fr>
Date: Thu, 23 Oct 2025 11:38:43 +0200
References: <0e5f0dbff5cf4bcf48f7ac9d829e178f@stamm-wilbrandt.de> <aOwKVfNxQcLiVYu5@seventeen> <97ec5bc016a560ddd037faec9620ebc2@stamm-wilbrandt.de> <aPjvv3ONOLE3BeIt@seventeen> <9fb1b240-b9ee-46bb-bad1-73cbf5a07ed0@gmail.com> <888cdbfb-57a5-ea0a-7d74-29a23827454e@math.u-bordeaux.fr> <aPnoFJ8WiRaSXEB3@seventeen>

Second attempt at a patch, the first was wrong. Replace the computation of p1 by

p1 = gsub(gmul(pmd, mulcxI(gsqr(zn))), gmul(s, glog(zn, prec)));
p1 = gmul(gexp(p1, prec), gmul(aleps, gadd(x, ix)));

This at least gives the right result for the zero at height 10^11, and does not crash at 10^21.

Best,

Henri

Follow-Ups:
- Re: Question on finding a Riemann Zeta function zero for high values of s
  - From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>

References:
- First non-trivial PARI/GP script from chatgpt session
  - From: hermann@stamm-wilbrandt.de
- Re: First non-trivial PARI/GP script from chatgpt session
  - From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
- Re: First non-trivial PARI/GP script from chatgpt session
  - From: hermann@stamm-wilbrandt.de
- Re: First non-trivial PARI/GP script from chatgpt session
  - From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
- Question on finding a Riemann Zeta function zero for high values of s
  - From: American Citizen <website.reader3@gmail.com>
- Re: Question on finding a Riemann Zeta function zero for high values of s
  - From: "Cohen Henri" <Henri.Cohen@math.u-bordeaux.fr>
- Re: Question on finding a Riemann Zeta function zero for high values of s
  - From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>