On the distribution of consecutive square-free primitive roots modulo $p$

Liu, Huaning, and Dong, Hui. "On the distribution of consecutive square-free primitive roots modulo $p$." Czechoslovak Mathematical Journal 65.2 (2015): 555-564. <http://eudml.org/doc/270106>.

@article{Liu2015,
abstract = {A positive integer $n$ is called a square-free number if it is not divisible by a perfect square except $1$. Let $p$ be an odd prime. For $n$ with $(n,p)=1$, the smallest positive integer $f$ such that $n^f \equiv 1 \hspace\{4.44443pt\}(\@mod \; p)$ is called the exponent of $n$ modulo $p$. If the exponent of $n$ modulo $p$ is $p-1$, then $n$ is called a primitive root mod $p$. Let $A(n)$ be the characteristic function of the square-free primitive roots modulo $p$. In this paper we study the distribution \[ \sum \_\{n\le x\}A(n)A(n+1), \] and give an asymptotic formula by using properties of character sums.},
author = {Liu, Huaning, Dong, Hui},
journal = {Czechoslovak Mathematical Journal},
keywords = {square-free; primitive root; square sieve; character sum},
language = {eng},
number = {2},
pages = {555-564},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the distribution of consecutive square-free primitive roots modulo $p$},
url = {http://eudml.org/doc/270106},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Liu, Huaning
AU - Dong, Hui
TI - On the distribution of consecutive square-free primitive roots modulo $p$
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 2
SP - 555
EP - 564
AB - A positive integer $n$ is called a square-free number if it is not divisible by a perfect square except $1$. Let $p$ be an odd prime. For $n$ with $(n,p)=1$, the smallest positive integer $f$ such that $n^f \equiv 1 \hspace{4.44443pt}(\@mod \; p)$ is called the exponent of $n$ modulo $p$. If the exponent of $n$ modulo $p$ is $p-1$, then $n$ is called a primitive root mod $p$. Let $A(n)$ be the characteristic function of the square-free primitive roots modulo $p$. In this paper we study the distribution \[ \sum _{n\le x}A(n)A(n+1), \] and give an asymptotic formula by using properties of character sums.
LA - eng
KW - square-free; primitive root; square sieve; character sum
UR - http://eudml.org/doc/270106
ER -