Short incomplete Gauss sums and rational points on metaplectic horocycles

Akarsu E.

INTERNATIONAL JOURNAL OF NUMBER THEORY, cilt.10, ss.1553-1576, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1142/s1793042114500444
  • Dergi Adı: INTERNATIONAL JOURNAL OF NUMBER THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1553-1576
  • Anahtar Kelimeler: Gauss sums, metaplectic group, horocycles, CENTRAL LIMIT-THEOREM, ASYMPTOTIC APPROXIMATION, EQUIDISTRIBUTION, PROOF
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Hayır

Özet

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).