20/01/10 03:39:04.79 oggcaPLw.net
>>586
>>594
こんなん見つけたんですけど・・・
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Vesselin Dimitrov says:
September 19, 2012 at 9:28 am
Mochizuki claims the strongest version of ABC that one could think of. (In particular, the effective one, and with the exponent 1 + epsilon).
See Theorem A on p. 3 of his fourth paper (ABC with exponent 1+epsilon is a standard consequence of this).
As for an explicit effective statement, take a look at the inequality asserted on page 23.
It concerns Szpiro’s inequality 1/6 log(D) < (1+epsilon) log(N) + Const. for the minimal discriminant D and conductor E of a (semistable) elliptic curve E.
Here, log q on the left-hand side is precisely log(D).
The f on the right-hand side is our conductor N, and the other term is a constant since we are concentrating on the single number field Q.
In section 2, the full ABC conjecture is deduced, in an effective manner (by the paper [GenEll]), from this effective (Szpiro) inequality.
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Vesselin Dimitrov says:
September 21, 2012 at 9:08 am
@Nick Nazari: If Mochizuki’s work is correct (and this is a pretty big “If”…), it would certainly yield a new proof of FLT.