[seqfan] Re: Looking for a paper from J London Math Soc 1930

Neil Sloane njasloane at gmail.com
Tue Nov 29 20:09:33 CET 2016


Juan,  Thank you very much for that reference!  I have added a comment to
A106867.

I agree that the Math Review makes it very likely that van der Blij gives a
proof.





Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Tue, Nov 29, 2016 at 1:31 PM, Juan Arias de Reyna <arias at us.es> wrote:

>
> Relevant the paper:
>
> MR0052462 Reviewed <http://ams.u-strasbg.fr/mathscinet/help/fullitem_help_
> full.html#review>
> van der Blij, F. <http://ams.u-strasbg.fr/mathscinet/search/author.html?
> mrauthid=38020>
> Binary quadratic forms of discriminant −23.
> Nederl. Akad. Wetensch. Proc. Ser. A. 55 = Indagationes Math. 14, (1952).
> 498–503.
>
> I think the relation, or something very similar,  is proved there.
> Best regards,
> Juan Arias de Reyna
>
> > El 29 nov 2016, a las 19:18, Neil Sloane <njasloane at gmail.com> escribió:
> >
> > Sean, Jean-Paul:   Thank you very much for sending the paper!  Even
> Rutgers
> > didn't have access to it.
> >
> > The sequence I was looking for, in Wilton's Table II, turns out to match
> > A106867 (at least at the start) .
> >
> > This is a bit of a surprise since the defn. of A106867 is
> > Primes of the form 2*x^2+x*y+3*y^2.
> > and there is a comment saying:
> > Primes p such that the polynomial x^3-x-1 is irreducible over Zp. The
> > polynomial discriminant is also -23.
> >
> > On the other hand, Wilton's definition is
> > Primes p such that Ramanujan tau(p) = A000594(p) == -1 (mod 23).
> >
> > Is it obvious that these are the same?  Since A106867 has a b-file from
> Ray
> > Chandler with 10000 terms,
> > it would be easy to check if they agree out that far.
> >
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> >
> > On Tue, Nov 29, 2016 at 1:03 PM, Sean A. Irvine <sairvin at gmail.com>
> wrote:
> >
> >> I have sent Neil the requested paper.
> >>
> >>
> >> On 30 November 2016 at 06:44, Neil Sloane <njasloane at gmail.com> wrote:
> >>
> >>> Can anyone get hold of a copy of
> >>>
> >>> Wilton, John Raymond. "Congruence properties of Ramanujan's function τ
> >>> (n)." *Proceedings of the London Mathematical Society* 2.1 (1930):
> 1-10.
> >>>
> >>> Lehmer says that Table II has a list of primes with a certain property
> >>> related to tau(n).
> >>>
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