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

Juan Arias de Reyna arias at us.es
Tue Nov 29 19:31:15 CET 2016


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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>> 
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