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There are some integrals related to the celebrated pair correlation conjecture of H. L. Montgomery. One of them is the integral introduced by Selberg related to estimating the variance of primes in short intervals: I read the last interesting paper of Yitang Zhang and it seems to me that the paper discusses the statistical distribution of Landau-Siegel zeros and primes as well. In the same time the correlation conjecture of H. L. Montgomery deals with estimation of the variance of primes.

My Question is: assuming Yitang Zhang latest results correct, to what extent these results would contribute to correlation conjecture of H. L. Montgomery?

Note: I ask kindly community to add tag for Yitang Zhang results or Yitang Zhang theorem.

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    $\begingroup$ Related Q&A. I'm not sure if anyone's directly addressed your query there, but a fair amount of discussion about the consequences of the result has already been had and may be ongoing. $\endgroup$
    – zibadawa timmy
    Commented Nov 10, 2022 at 7:32
  • $\begingroup$ @zibadawatimmy, Thanks for the link ,I already checked these questions but seems to me some consequences were adressed to be in general but here i asked for specific contribution which is not montioned there,namely,connection to HL Montgomery $\endgroup$
    – zeraoulia rafik
    Commented Nov 11, 2022 at 23:17
  • $\begingroup$ Note that pair correlation has been established unconditionally in a recent preprint by Suriajaya et al. $\endgroup$
    – Sylvain JULIEN
    Commented Jun 16, 2023 at 10:25
  • $\begingroup$ The considered preprint: arxiv.org/abs/2306.04799 $\endgroup$
    – Sylvain JULIEN
    Commented Jun 16, 2023 at 10:28

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