Biases in the prime number race of function fields
type: Item
instance of: scholarly article
title: Biases in the prime number race of function fields
zbMATH Open document ID: 1195.11124
author: Byungchul Cha
author: Seick Kim
published in: Journal of Number Theory
publication date: 2010-04-08T00:00:00Z
review text: Let \(\pi(a,m,N)=\#\{ P\mid P\equiv a\bmod m,\,\deg(P)=N\}\). In this paper, the main theorem gives an explicit description of the density \(\delta_{m;a_{1},\dots,a_{r}}\) of the subset \(\{X\in \mathbb{Z}\mid X>0,\sum_{N=1}^{X}\pi(a_{1},m,N)>\dots>\sum_{N=1}^{X}\pi(a_{r},m,N)\}\) of all positive integers in terms of the measure \(\mu(\{(x_1,\dots,x_r \in\mathbb{R}^{r}\mid x_1>\dots>x_r)\})\). This is a function field analog of the work of \textit{A. Feuerverger} and \textit{G. Martin} [Exp. Math. 9, No. 4, 535--570 (2000; Zbl 0976.11041)], who established such formula in the number field case, building up on the fundamental work of \textit{M. Rubinstein} and \textit{P. Sarnak} [Exp. Math. 3, 173--197 (1994; Zbl 0823.11050)].
reviewed by: Zaizhao Meng
Mathematics Subject Classification ID: 11N13
Mathematics Subject Classification ID: 11B25
Mathematics Subject Classification ID: 11T55
zbMATH DE Number: 5690737
zbMATH Keywords: Chebyshev's bias
zbMATH Keywords: prime number race
zbMATH Keywords: comparative number theory
zbMATH Keywords: linear independence
MaRDI profile type: Publication
full work available at URL: j.jnt.2009.09.015
OpenAlex ID: W2012674309
Wikidata QID: Q108368773
cites work: Chebyshev’s bias in function fields
cites work: Biases in the Shanks—Rényi Prime Number Race
cites work: Chebyshev's Bias
cites work: Prime Number Races
DOI: 10.1016/J.JNT.2009.09.015
description: scientific article; zbMATH DE number 5690737