---
res:
  bibo_abstract:
  - We prove that the average size of a mixed character sum (math. formular) (for
    a suitable smooth function w) is on the order of √x for all irrational real θ
    satisfying a weak Diophantine condition, where χ is drawn from the family of Dirichlet
    characters modulo a large prime r and where x 6 r. In contrast, it was proved
    by Harper that the average size is o(√x) for rational θ. Certain quadratic Diophantine
    equations play a key role in the present paper. @eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Victor
      foaf_name: Wang, Victor
      foaf_surname: Wang
      foaf_workInfoHomepage: http://www.librecat.org/personId=76096395-aea4-11ed-a680-ab8ebbd3f1b9
    orcid: 0000-0002-0704-7026
  - foaf_Person:
      foaf_givenName: Max
      foaf_name: Xu, Max
      foaf_surname: Xu
  bibo_doi: 10.1017/prm.2026.10123
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0308-2105
  - http://id.crossref.org/issn/1473-7124
  dct_language: eng
  dct_publisher: Cambridge University Press@
  dct_title: Average sizes of mixed character sums@
...