Short incomplete Gauss sums and rational points on metaplectic horocycles


Akarsu E.

INTERNATIONAL JOURNAL OF NUMBER THEORY, vol.10, pp.1553-1576, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10
  • Publication Date: 2014
  • Doi Number: 10.1142/s1793042114500444
  • Title of Journal : INTERNATIONAL JOURNAL OF NUMBER THEORY
  • Page Numbers: pp.1553-1576

Abstract

In this paper, we investigate the limiting behavior of short incomplete Gauss sums at random argument as the number of terms goes to infinity. We prove that the limit distribution is given by the distribution of theta sums and differs from the limit law for long Gauss sums studied by the author and Marklof. The key ingredient in the proof is an equidistribution theorem for rational points on horocycles in the metaplectic cover of SL(2, R).