18/09/27 06:23:32.93 xNwcF5GI.net
>>69 つづき
Yitang Zhang’s 54 page paper spends more time on material that is standard to the experts (in particular following the tradition common in analytic number theory to put all the routine lemmas needed later in the paper in a rather lengthy but straightforward early section),
but about six pages after all the lemmas are presented, Yitang has made a non-trivial observation, which is that bounded gaps between primes would follow if one could make any improvement to the Bombieri-Vinogradov theorem for smooth moduli.
(This particular observation was also previously made independently by Motohashi and Pintz, though not quite in a form that was amenable to Yitang’s arguments in the remaining 30 pages of the paper.)
This is not the deepest part of Yitang’s paper, but it definitely reduces the problem to a more tractable-looking one,
in contrast to the countless papers attacking some major problem such as the Riemann hypothesis in which one keeps on transforming the problem to one that becomes more and more difficult looking, until a miracle (i.e. error) occurs to dramatically simplify the problem.
From what I have read and heard, I gather that currently, the shortest “proof of concept” of a non-trivial result in an existing (i.e. non-IUTT) field in Mochizuki’s work is the 300+ page argument needed to establish the abc conjecture.
It seems to me that having a shorter proof of concept (e.g. <100 pages) would help dispel scepticism about the argument.
It seems bizarre to me that there would be an entire self-contained theory whose only external application is to prove the abc conjecture after 300+ pages of set up, with no smaller fragment of this setup having any non-trivial external consequence whatsoever.
(引用終り)
(参考 Yitang Zhang’s 54 page paperは、ガセか？ そも、この論文に日付無し)
URLﾘﾝｸ(citeseerx.ist.psu.edu)
Bounded gaps between primes - CiteSeerX Yitang Zhang