Geodesic
Some new sums related to D. H. Lehmer problem
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 915-922.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 \leq a_i \leq 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.
DOI : 10.1007/s10587-015-0217-y
Classification : 11L05, 11L40
Keywords: Lehmer number; analytic method; trigonometric sums; asymptotic formula 
@article{10_1007_s10587_015_0217_y,
     author = {Zhang, Han and Zhang, Wenpeng},
     title = {Some new sums related to {D.} {H.} {Lehmer} problem},
     journal = {Czechoslovak Mathematical Journal},
     pages = {915--922},
     publisher = {mathdoc},
     volume = {65},
     number = {4},
     year = {2015},
     doi = {10.1007/s10587-015-0217-y},
     mrnumber = {3441325},
     zbl = {06537700},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0217-y/}
}
TY  - JOUR
AU  - Zhang, Han
AU  - Zhang, Wenpeng
TI  - Some new sums related to D. H. Lehmer problem
JO  - Czechoslovak Mathematical Journal
PY  - 2015
SP  - 915
EP  - 922
VL  - 65
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0217-y/
DO  - 10.1007/s10587-015-0217-y
LA  - en
ID  - 10_1007_s10587_015_0217_y
ER  - 
%0 Journal Article
%A Zhang, Han
%A Zhang, Wenpeng
%T Some new sums related to D. H. Lehmer problem
%J Czechoslovak Mathematical Journal
%D 2015
%P 915-922
%V 65
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0217-y/
%R 10.1007/s10587-015-0217-y
%G en
%F 10_1007_s10587_015_0217_y
Zhang, Han; Zhang, Wenpeng. Some new sums related to D. H. Lehmer problem. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 915-922. doi : 10.1007/s10587-015-0217-y. http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0217-y/

Cité par Sources :