20/04/14 22:57:16 mIlcNUlX.net
>>68
つづき
これか
ここは、SSの文書が公開された当時にも話題になったかも（＾＾
(C1) : Remark 5, “For fixed ... h(P) ? b.”: I can only say that it is a very challenging task to document the depth of my astonishment when I first read this Remark!
This Remark may be described as a breath-takingly (melo ?) dramatic self-declaration, on the part of SS, of their profound ignorance of the elementary theory of heights, at the advanced undergraduate/beginning graduate level.
Indeed, the finiteness statement at the beginning of the paragraph follows immediately, by considering the j-invariant
(say, multiplied by a suitable positive integer N, which depends only on d and b)
of the elliptic curve under consideration, from the finiteness of the set of complex numbers that satisfy a monic polynomial equation of degree d with coefficients ∈ Z of absolute value ? C, for some fixed real number C that depends only on d and b.
To repeat, this sort of argument lies well within the framework of advanced undergraduate/beginning graduate-level mathematics.
つづく