Pierre Charollois on Thu, 27 Apr 2023 12:54:58 +0200


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Re: Recognizing numbers using PARI/GP

I am in awe with what you all achieved as a community, and simply want to emphasize this :
Kevin Lucas came up with an 8-digit number like 2.0298832, and the combination of (you guys + google) enabled the outcome of a specific zeta value as a guess.

This is simply amazing experimental maths.
Congratulations !

Best regards,

Pierre


Le jeu. 27 avr. 2023 à 11:51, Bill Allombert <Bill.Allombert@math.u-bordeaux.fr> a écrit :
On Thu, Apr 27, 2023 at 02:27:13AM +0200, Karim Belabas wrote:
> From Bill's first formula (and Milnor's proof of it given in the
> Wikipedia article), you can express this in terms of Lobachevsky's function
> and in turn get your expected relation to Dedekind zeta function:
>
> ? lfun(x^2+3,2)/zeta(2) * sqrt(27) / 2
> %1 = 2.0298832128193072500424051085490405719

So you see it is a multiplicative formula as expected,  so you could find it with

? lindep([log(z),log(lfun(-3,2)),log(zeta(2)),log(2),log(3)])
%71 = [-2,2,0,-2,3]~

so z^2 = lfun(-3,2)^2*2^-2*3^3 and
z = 3*sqrt(3)/2*lfun(-3,2)

Cheers,
--
Bill Allombert
Ingénieur de recherche en calcul scientifique ❄
CNRS/IMB UMR 5251