Square-full polynomials in short intervals and in arithmetic progressions

被引：6
|
作者：
Roditty-Gershon E. [1 ]
机构：
[1] School of Mathematics, University of Bristol, Bristol
来源：
Research in Number Theory | / 3卷 / 1期
基金：
英国工程与自然科学研究理事会;
关键词：
Arithmetic Progression; Equidistribution Result; Dirichlet Character; Inverse Root; Function field Setting;
D O I：
10.1007/s40993-016-0066-2
中图分类号：
学科分类号：
摘要：
We study the variance of sums of the indicator function of square-full polynomials in both arithmetic progressions and short intervals. Our work is in the context of the ring Fq[ T] of polynomials over a finite field Fq of q elements, in the limit q→ ∞. We use a recent equidistribution result due to N. Katz to express these variances in terms of triple matrix integrals over the unitary group, and evaluate them. © 2017, The Author(s).
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