Thanks, Victor! Kiran's senior thesis looks very useful. --Dan On 2012-12-15, at 12:18 PM, Victor Miller wrote:
Look at Chapter 4 in http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.3926
Victor
On Sat, Dec 15, 2012 at 2:33 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Wikipedia states:
I) << [I]f τ is any element of an imaginary quadratic field with positive imaginary part (so that j is defined) then is an algebraic integer.
and elsewhere one finds that, in particular,
II) << j((-1 + sqrt(-163))/2) = (-640320)^3
which is apparently a special case of the fact that in general,
III) << The value of j at an element of an imaginary quadratic field is an algebraic integer whose degree is the class number of that field.
Further, II) is apparently related to the fact that the elliptic curve C / Z[(-1 + sqrt(-163))/2)] has "complex multiplication".
There seem to be ample references to books where these facts are proven, but I haven't found any to online references, or journal articles.
Can anyone please either explain these facts or else point me to some online reference(s) or journal article(s) where these facts are explained?
Many thanks,
Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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