POISSON SPACING STATISTICS FOR VALUE SETS OF POLYNOMIALS

被引：5
|
作者：
Kurlberg, Paer [1 ]
机构：
[1] Royal Inst Technol, Dept Math, SE-10044 Stockholm, Sweden
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2009年 / 5卷 / 03期
基金：
美国国家科学基金会; 瑞典研究理事会;
关键词：
Poisson spacings; correlation function; QUADRATIC RESIDUES;
D O I：
10.1142/S1793042109002237
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
If f is a non-constant polynomial with integer coefficients and q is an integer, we may regard f as a map from Z/qZ to Z/qZ. We show that the distribution of the (normalized) spacings between consecutive elements in the image of these maps becomes Poissonian as q tends to infinity along any sequence of square free integers such that the mean spacing modulo q tends to infinity.
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页码：489 / 513
页数：25
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