---
res:
  bibo_abstract:
  - "Gross and Smith have put forward generalizations of Hardy–Littlewood twin prime\r\nconjectures
    for algebraic number fields. We estimate the behaviour of sums of a singular series
    that arises in these conjectures, up to lower-order terms. More exactly,\r\nwhere
    S(η) is the singular series, we find asymptotic formulas for smoothed sums of\r\nS(η)−1.
    Based upon Gross and Smith’s conjectures, we use our result to suggest that\r\nfor
    large enough ‘short intervals’ in an algebraic number field K, the variance of
    counts\r\nof prime elements in a random short interval deviates from a Cramér
    model prediction\r\nby a universal factor, independent of K. The conjecture over
    number fields generalizes\r\na classical conjecture of Goldston and Montgomery
    over the integers. Numerical data\r\nare provided supporting the conjecture.@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
  - foaf_Person:
      foaf_givenName: Brad
      foaf_name: Rodgers, Brad
      foaf_surname: Rodgers
  - foaf_Person:
      foaf_givenName: Edva
      foaf_name: Roditty-Gershon, Edva
      foaf_surname: Roditty-Gershon
  bibo_doi: 10.1007/s11139-022-00561-9
  bibo_issue: '2'
  bibo_volume: 58
  dct_date: 2022^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1382-4090
  - http://id.crossref.org/issn/1572-9303
  dct_language: eng
  dct_publisher: Springer Nature@
  dct_subject:
  - Primes
  - Short intervals
  - Ramanujan sums
  - Singular series
  - Number fields
  dct_title: Sums of singular series and primes in short intervals in algebraic number
    fields@
...