The value distribution of incomplete Gauss sums
The value distribution of incomplete Gauss sums
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不完全高斯和的值分布
DOI：
10.1112/s0025579312001179
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发表时间：
2012
期刊：
影响因子：
0.8
通讯作者：
J. Marklof
中科院分区：
文献类型：
--
作者：
Emek Demirci Akarsu;J. Marklof
众所周知，用项的平方根数归一化的经典高斯和只取有限多个值。如果把求和的范围限制在一个子区间内，就会出现一个更丰富的结构。我们证明了这类不完全高斯和的值分布的一个极限定律。极限分布由某一族周期函数的分布给出。我们的结果补充了Oskolkov关于不完全Gauss和的逐点界，以及Jurkat和van Horne和第二作者关于二次Weyl和(theta和)的极限定理。
It is well known that the classical Gauss sum, normalized by the square-root number of terms, takes only finitely many values. If one restricts the range of summation to a subinterval, a much richer structure emerges. We prove a limit law for the value distribution of such incomplete Gauss sums. The limit distribution is given by the distribution of a certain family of periodic functions. Our results complement Oskolkov’s pointwise bounds for incomplete Gauss sums as well as the limit theorems for quadratic Weyl sums (theta sums) due to Jurkat and van Horne and the second author.