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Karim Belabas on Thu, 27 Apr 2023 02:40:53 +0200
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Re: Recognizing numbers using PARI/GP
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- To: pari-users@pari.math.u-bordeaux.fr
- Subject: Re: Recognizing numbers using PARI/GP
- From: Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>
- Date: Thu, 27 Apr 2023 02:39:14 +0200
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* Karim Belabas [2023-04-27 02:27]:
> 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
Forgot to mention another (simpler?) expression for this, also
explained in Milnor's paper:
? 3 * imag( dilog(exp(2*I*Pi/3)) )
%2 = 2.0298832128193072500424051085490405719
Cheers,
K.B.
--
Pr Karim Belabas, U. Bordeaux, Vice-président en charge du Numérique
Institut de Mathématiques de Bordeaux UMR 5251 - (+33) 05 40 00 29 77
http://www.math.u-bordeaux.fr/~kbelabas/