[seqfan] Re: Numbers and 'forms'.
Charles Greathouse
charles.greathouse at case.edu
Sat Jun 28 01:44:50 CEST 2014
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
>
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