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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
Article

Abstract

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 .

Keywords

Arbitrary Element Prime Order Additive Character Arbitrary Subset Multiplicative Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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