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

[Neil Sloane]

I would like to say that I really appreciate the response from
the Sequence Fans to my questions. Replies from (I think) New Zealand,
France, and Spain. Wow!
The world may be falling apart, politically and ecologically, but the OEIS
is a good way to escape
the troubles.

By the way, here is how I came across the Wilton paper.

When I retired from AT&T/Bell Labs in 2012, I moved a large
number of boxes of papers home. I am slowly going through them, finding
many interesting things.
These are papers that I have collected over the past 55 years.

There are many new sequences buried in these old papers.
If you look at the sequences I've added to the OEIS in the past year, you
will see many from the distant past. A278567 is a recent example.
See also the mysterious A278575.

In one box there were a lot of offprints that used to belong
to D H Lehmer in Berkeley. (Remember in the old days when
you published a paper you would get 50 free offprints to give out
to your friends?)  Some of these are over 100 years old.

For example, there is an offprint Ueber Fareysche Doppelreihen by Heinrich
Made,
from Giessen, 1903.

There are many papers by Lehmer himself, one of which is "The vanishing of
Ramanujan's function tau(n)" from 1947, which mentions the Wilton paper.  I
have annotated it  (the Lehmer paper) with references to the sequences it
mentions, and I'm going to scan it and add it to all those sequences.
There are two other sequences in the Wilton paper which are new, and later
today they will be
A278578, A278579.




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 2:09 PM, Neil Sloane <njasloane at gmail.com> wrote:

> 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/maths
>> cinet/help/fullitem_help_full.html#review>
>> van der Blij, F. <http://ams.u-strasbg.fr/maths
>> cinet/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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>> >
>> > --
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>>
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>
>