TITLE: Yitang Zhang's preprint on Landau-Siegel zeros
QUESTION [45 upvotes]: The recent sensational news on bounded gaps between primes made me wonder: what is the status of Yitang Zhang's earlier arXiv preprint on Landau-Siegel zeros? If this result is correct, then (in my opinion) it is even bigger news for analytic number theory. Has anyone checked this paper carefully?

REPLY [11 votes]: I started a careful study of the paper but stopped after already stumbling over Lemma 2.3. Let me cite from an email in Jan 2008

I can't follow the proof of Lemma 2.3, which is a key
  in proving Lemmas 2.4-2.6 and therefore also Prop. 2.7
  and therefore also the Theorem:
  As far as I understand, the paper estimates (see last line on
  page 8) the Supremum (over the s in Omega_1) of the
  left sum via standard integral-estimation by L^2 times
  the supremum (over the w in R_1) of the respected sum.
  The last equals the sum at a special w in R_1
  (Maximum-principle of continuous functions), but this
  w is (highly) dependent on the psi. Thats why I dont
  understand how one can then use the great sieve as in
  page 9 top in order to estimate the initial sum at the
  left of 2.11, because the great sieve applies only
  when the coefficients are (of course) independent of
  psi.
  Contrary, if the way of proving Lemma 2.3 was
  actually as sketched above, then I dont see it
  necessary to go the extra way over the integral, but
  one could estimate immediately. That's why I think I
  may have missed a point.
  ...
  (I don't think
  that a variation of the statement could help, since
  Lemmas 2.4-2.6 are using very precisely the full
  statement of Lemma 2.3, the same with Prop. 2.7).

Yitang Zhang should at least provide a respective comment at his arxiv-article where/how incomplete the paper is. Frankly put, not being fully transparent about the state of this work and thus have other people spend their time on it (not knowing where it is lacking) is absolutely ridiculous.