Some new sums related to D. H. Lehmer problem

Zhang, Han, and Zhang, Wenpeng. "Some new sums related to D. H. Lehmer problem." Czechoslovak Mathematical Journal 65.4 (2015): 915-922. <http://eudml.org/doc/276093>.

@article{Zhang2015,
abstract = {About Lehmer’s number, many people have studied its various properties, and obtained a series of interesting results. In this paper, we consider a generalized Lehmer problem: Let $p$ be a prime, and let $N(k; p)$ denote the number of all $1 \le a_i \le p - 1 $ such that $a_1a_2 \cdots a_k \equiv 1 ~\@mod \;p$ and $2 \mid a_i + \bar\{a\}_i + 1,$$i = 1, 2, \cdots , k$. The main purpose of this paper is using the analytic method, the estimate for character sums and trigonometric sums to study the asymptotic properties of the counting function $N(k; p),$ and give an interesting asymptotic formula for it.},
author = {Zhang, Han, Zhang, Wenpeng},
journal = {Czechoslovak Mathematical Journal},
keywords = {Lehmer number; analytic method; trigonometric sums; asymptotic formula},
language = {eng},
number = {4},
pages = {915-922},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some new sums related to D. H. Lehmer problem},
url = {http://eudml.org/doc/276093},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Zhang, Han
AU - Zhang, Wenpeng
TI - Some new sums related to D. H. Lehmer problem
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 4
SP - 915
EP - 922
AB - About Lehmer’s number, many people have studied its various properties, and obtained a series of interesting results. In this paper, we consider a generalized Lehmer problem: Let $p$ be a prime, and let $N(k; p)$ denote the number of all $1 \le a_i \le p - 1 $ such that $a_1a_2 \cdots a_k \equiv 1 ~\@mod \;p$ and $2 \mid a_i + \bar{a}_i + 1,$$i = 1, 2, \cdots , k$. The main purpose of this paper is using the analytic method, the estimate for character sums and trigonometric sums to study the asymptotic properties of the counting function $N(k; p),$ and give an interesting asymptotic formula for it.
LA - eng
KW - Lehmer number; analytic method; trigonometric sums; asymptotic formula
UR - http://eudml.org/doc/276093
ER -