亚纯整圈上的短不完全Gauss和与有理点
Short incomplete Gauss sums and rational points on metaplectic horocycles
摘要：
本文研究了随机变元短不完全高斯和在项数趋于无穷大时的极限行为。我们证明了极限分布是由θ和的分布给出的，并且不同于作者和Marklof研究的长高斯和的极限律。证明的关键是SL（2，R）的亚复盖中的horocycles上的有理点的等分布定理。
英文摘要：
In the present paper we investigate the limiting behaviour 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).
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