---
res:
  bibo_abstract:
  - "Montgomery and Soundararajan showed that the distribution of ψ(x+H)−ψ(x), for
    0≤ x ≤ N, is approximately normal with mean ∼ H and variance ∼ H log(N/H), when
    N\r\nδ ≤ H ≤ N\r\n1−δ\r\n. Their work depends\r\non showing that sums Rk (h) of
    k-term singular series are µk (−h log h + Ah)\r\nk/2 + Ok (h\r\nk/2−1/(7k)+ε\r\n),\r\nwhere
    A is a constant and µk are the Gaussian moment constants. We study lower-order
    terms in the size\r\nof these moments. We conjecture that when k is odd, Rk (h)
    ≍ h\r\n(k−1)/2\r\n(log h)\r\n(k+1)/2\r\n. We prove an upper\r\nbound with the
    correct power of h when k = 3, and prove analogous upper bounds in the function
    field\r\nsetting when k = 3 and k = 5. We provide further evidence for this conjecture
    in the form of numerical\r\ncomputations.@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: 10.2140/ant.2025.19.617
  bibo_issue: '4'
  bibo_volume: 19
  dct_date: 2025^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1937-0652
  - http://id.crossref.org/issn/1944-7833
  dct_language: eng
  dct_publisher: Mathematical Sciences Publishers@
  dct_title: Odd moments in the distribution of primes@
...