---
res:
  bibo_abstract:
  - "In 1976, Gallagher showed that the Hardy–Littlewood conjectures on prime k-tuples
    imply that the\r\ndistribution of primes in log-size intervals is Poissonian.
    He did so by computing average values\r\nof the singular series constants over
    different sets of a fixed size k contained in an interval [1,h]\r\nas h → ∞, and
    then using this average to compute moments of the distribution of primes. In this\r\npaper,
    we study averages where k is relatively large with respect to h. We then apply
    these averages\r\nto the tail of the distribution. For example, we show, assuming
    appropriate Hardy–Littlewood\r\nconjectures and in certain ranges of the parameters,
    the number of intervals [n,n + λlogx] with\r\nn ≤ x containing at least k primes
    is ≪ x exp(−k/(λe)).@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Vivian Zieve
      foaf_name: Kuperberg, Vivian Zieve
      foaf_surname: Kuperberg
      foaf_workInfoHomepage: http://www.librecat.org/personId=c3bac823-112d-11f0-a3f5-c264f852e697
  bibo_doi: 10.1093/qmath/haad030
  bibo_issue: '4'
  bibo_volume: 74
  dct_date: 2023^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0033-5606
  - http://id.crossref.org/issn/1464-3847
  dct_language: eng
  dct_publisher: Oxford University Press@
  dct_title: Sums of singular series with large sets and the tail of the distribution
    of primes@
...