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

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Thu, Oct 23, 2025 at 11:33:05AM +0200, Bill Allombert wrote:
> On Thu, Oct 23, 2025 at 09:15:45AM +0200, Cohen Henri wrote:
> > 
> > Sorry, you are right, my patch breaks things. The unpatched code does give the correct
> > result. I will look into it again.
> 
> I suggest a different patch below where instead of
> exp(p1)*p2 we compute exp(p1+log(p2))
> so cancellation between p1 and log(p2) can occur.
> 
> See the branch henri-lfunlarge_overflow

My patch gives this (on 20 cores):

? s = 1/2 +  1370919909931995308226.68016095*I
? zeta(s)
%2 = 4.0536436970172441408698440140242774312E-8+2.4195172994094734771061685252890615819E-8*I
? ##
  ***   last result: cpu time 3h, 5min, 29,246 ms, real time 9min, 24,947 ms.

I will try Henri 2nd patch (which is close to mine).

Cheers,
Bill