[seqfan] Re: Numbers and 'forms'.

[Neil Sloane]

Well, in the OEIS we follow Buell, Cox, et al., and use the obvious meaning
of "represent". I know Andrew well, and in fact I was on his thesis
committee.

I've just about finished my
survey of seqs arising from binary quadratic forms - see next message.

There is lots of work that needs doing.

Neil


On Fri, Jun 27, 2014 at 7:44 PM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> It seems clear that multiple definitions are in use. The best thing we can
> do is be explicit in the individual sequences so neither camp will be
> confused.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
>
> On Fri, Jun 27, 2014 at 6:31 PM, Peter Luschny <peter.luschny at gmail.com>
> wrote:
>
> > NJAS> Peter said " a form represents n by
> > NJAS> integers x, y if and only if x != 0."
> >
> > Yes, I said it, but I did not invent this definition.
> >
> > NJAS> The authorities disagree.
> > NJAS> [...] David Cox, "Primes of the Form x^2+ny^2"
> > NJAS> [...] Buell, Binary Quadratic Forms
> >
> > I took the definition from Andrew Sutherland [1] who is
> > Principal Research Scientist in Computational Number Theory
> > at the MIT and was recently awarded the Selfridge Prize
> > (by the way like John Voight).
> >
> > So at least it is worth to listen to his arguments.
> >
> > To see Sutherland's arguments in place look at his
> > lectures "Introduction to Arithmetic Geometry" [2] and [3]
> > which were chosen as MIT course ware. The relevant
> > chapter is [4]. See definition 9.7, example 9.8 and
> > the comment following it.
> >
> > Perhaps I am missing something and I am not an expert
> > who can evaluate diligently the relative merits of the
> > two definitions but judging from the context in Sutherland's
> > lecture I am inclined to follow his definition.
> >
> > Peter
> >
> > [1] https://math.mit.edu/people/profile.php?pid=272
> > [2]
> >
> http://ocw.mit.edu/courses/mathematics/18-782-introduction-to-arithmetic-geometry-fall-2013/
> > [3]
> >
> http://ocw.mit.edu/courses/mathematics/18-782-introduction-to-arithmetic-geometry-fall-2013/lecture-notes/
> > [4]
> >
> http://ocw.mit.edu/courses/mathematics/18-782-introduction-to-arithmetic-geometry-fall-2013/lecture-notes/MIT18_782F13_lec9.pdf
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
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>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

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