STATISTICS OF PRIME DIVISORS IN FUNCTION FIELDS

被引：5

作者：

Rhoades, Robert C. ^{[1
]}

机构：

[1] Ecole Polytech Fed Lausanne, Dept Math, CH-1015 Lausanne, Switzerland

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2009年 / 5卷 / 01期

关键词：

Divisors; factorization; Poisson distribution; function fields;

D O I：

10.1142/S1793042109001980

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the prime divisors of a random polynomial in F-q[t] are typically "Poisson distributed". This result is analogous to the result in Z of Granville [1]. Along the way, we use a sieve developed by Granville and Soundararajan [2] to give a simple proof of the Erdos-Kac theorem in the function field setting. This approach gives stronger results about the moments of the sequence {omega(f)}(f is an element of Fq)[t] than was previously known, where omega(f) is the number of prime divisors of f.

引用

页码：141 / 152

页数：12