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

[American Citizen <website.reader3@gmail.com>]

Thanks Bill, that patch works.

We now get

> Zero number    Imaginary part
> 1048449113    388858885.3843374064120148806916184198555
> 388858885.384337406412014880691618419855483458064719603521 (GP Pari)
>
> 1048449114    388858886.0022851217767970582610330824021
> 1048449115    388858886.0023936897027167200756700895163
>
> 1048449116    388858886.6907450529570780149380015280575
> 388858886.690745052957078014938001528057403962286595277234 (GP Pari)
Using the LMFMB data at 
https://www.lmfdb.org/zeros/zeta/?limit=4&N=1048449113

But my simple convergence for the middle two terms is NOT converging, as 
the top and bottom ones did quite well in a reasonable time, but I 
expect that the reason is because these two zeroes are very close in value.

I am not familiar with Newton's method in complex analysis, to be able 
to converge these middle 2 terms to 57 digits accuracy.

But the data looks good now, but I am not going to check all 
103,800,788,359 zeros here, it's hard enough writing a python program to 
parse the data from the folder and then use the platt.py reader to 
locate Lehmer pairs and output those. I did put in a request for the 
website to create a list of Lehmer pairs for their voluminous Riemann 
Zeroes database, and hope that they consider this as reasonable.

Randall

On 10/23/25 02:33, 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
>
> Cheers,
> Bill.