[seqfan] Re: Numbers and 'forms'.

[Charles Greathouse]

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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