INTERNATIONAL JOURNAL OF NUMBER THEORY, vol.10, pp.1553-1576, 2014 (SCI-Expanded)
Article / Article
INTERNATIONAL JOURNAL OF NUMBER THEORY
Science Citation Index Expanded (SCI-EXPANDED), Scopus
Gauss sums, metaplectic group, horocycles, CENTRAL LIMIT-THEOREM, ASYMPTOTIC APPROXIMATION, EQUIDISTRIBUTION, PROOF
Recep Tayyip Erdoğan University Affiliated:
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).