[seqfan] Re: Numbers and 'forms'.

Peter Luschny peter.luschny at gmail.com
Sat Jun 28 00:31:37 CEST 2014

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.


[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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