Journal d'Analyse Mathématique

, Volume 115, Issue 1, pp 51–70 | Cite as

Exponential sum estimates over a subgroup in an arbitrary finite field

  • J. Bourgain
  • A. Glibichuk


Let F q be the finite field consisting of q = p r elements and yy an additive character of the field F q . Take an arbitrary multiplicative subgroup H of size |H| > q C/(log log q) for some constant C > 0 not largely contained in any multiplicative shift of a subfield. We show that |Σ hH yy(h)| = o(|H|). This means that H is equidistributed in F q .


Arbitrary Element Prime Order Additive Character Arbitrary Subset Multiplicative Subgroup 
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Copyright information

© Hebrew University Magnes Press 2011

Authors and Affiliations

  1. 1.Institute for Advanced StudyPrincetonUSA
  2. 2.Insituto de MatemáticasUniversidad Nacional Autónoma de México CampusmoreliaMoreliamicaocánMéxico

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