Inter-universal geometry と ABC予想 (応援スレ) 63at MATH

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483:ｨ +∞. (iii) (Uniform abc) C(K, ε) = Oε(1). It is remarked in p. 510 of Granville?Stark [7] that Conjecture 5.2 (iii) follows from Vojta’s General Conjecture under the assumption that [K : Q] is bounded; consequently, so does (i) and (ii).10 Remark 5.3. See also Remark 2.2.3 of Mochizuki’s “IUT IV” [14], in which it is explained that the calculations of Corollary 2.2 (ii), (iii) of IUT IV can be regarded as a sort of “weak” version of uniform abc. Such version, however, is much weaker than the O-weak uniform abc in Conjecture 5.2 (i), and thus, in principle, one is not able to deduce “no Siegel zeros” from Corollary 2.2 of [14] by using the methods we are employing here. (引用終り) 以上

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