下記、Goldfeld, Modular forms, elliptic curves, and the ABC-conjecture が、なかなか良いね

https://ja.wikipedia.org/wiki/%E3%82%B9%E3%83%94%E3%83%AD%E4%BA%88%E6%83%B3
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脚注
3^ D. Goldfeld, Modular forms, elliptic curves, and the ABC-conjecture.
http://www.math.columbia.edu/~goldfeld/
DORIAN GOLDFELD
http://www.math.columbia.edu/~goldfeld/Papers.html
Selected Publications of Dorian Goldfeld
http://www.math.columbia.edu/~goldfeld/ABC-Conjecture.pdf
Modular Forms, Elliptic Curves, and the ABC Conjecture, (2003) pdf

§1. The ABC-Conjecture.
The ABC-conjecture was first formulated by David Masser and Joseph Osterl´e (see
[Ost]) in 1985. Curiously, although this conjecture could have been formulated in the
last century, its discovery was based on modern research in the theory of function fields
and elliptic curves, which suggests that it is a statement about ramification in arithmetic
algebraic geometry. The ABC-conjecture seems connected with many diverse and well
known problems in number theory and always seems to lie on the boundary of what is
known and what is unknown. We hope to elucidate the beautiful connections between
elliptic curves, modular forms and the ABC-conjecture.
Conjecture (ABC). Let A, B, C be non-zero, pairwise relatively prime, rational integers
satisfying A + B + C = 0. Define
N = Πp|ABC p
to be the squarefree part of ABC. Then for every ε > 0, there exists κ(ε) > 0 such that
max(|A|, |B|, |C|) < κ(ε)N1+ε.
A weaker version of the ABC-conjecture (with the same notation as above) may be given
as follows.
Conjecture (ABC) (weak). For every ε > 0, there exists κ(ε) > 0 such that
|ABC| 1/3 < κ(ε)N1+ε.

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