Geodesic
On the $k$-polygonal numbers and the mean value of Dedekind sums
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 409-415 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

For any positive integer $k\geq 3$, it is easy to prove that the \mbox {$k$-polygonal} numbers are $a_n(k)= (2n+n(n-1)(k-2))/2$. The main purpose of this paper is, using the properties of Gauss sums and Dedekind sums, the mean square value theorem of Dirichlet \mbox {$L$-functions} and the analytic methods, to study the computational problem of one kind mean value of Dedekind sums $S(a_n(k)\overline {a}_m(k), p)$ for \mbox {$k$-polygonal} numbers with $1\leq m,n\leq p-1$, and give an interesting computational formula for it.
For any positive integer $k\geq 3$, it is easy to prove that the \mbox {$k$-polygonal} numbers are $a_n(k)= (2n+n(n-1)(k-2))/2$. The main purpose of this paper is, using the properties of Gauss sums and Dedekind sums, the mean square value theorem of Dirichlet \mbox {$L$-functions} and the analytic methods, to study the computational problem of one kind mean value of Dedekind sums $S(a_n(k)\overline {a}_m(k), p)$ for \mbox {$k$-polygonal} numbers with $1\leq m,n\leq p-1$, and give an interesting computational formula for it.
DOI : 10.1007/s10587-016-0264-z
Classification : 11L05, 11L10
Keywords: Dedekind sums; mean value; computational problem; $k$-polygonal number; analytic method 
@article{10_1007_s10587_016_0264_z,
     author = {Guo, Jing and Li, Xiaoxue},
     title = {On the $k$-polygonal numbers and the mean value of {Dedekind} sums},
     journal = {Czechoslovak Mathematical Journal},
     pages = {409--415},
     year = {2016},
     volume = {66},
     number = {2},
     doi = {10.1007/s10587-016-0264-z},
     mrnumber = {3519610},
     zbl = {06604475},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-016-0264-z/}
}
TY  - JOUR
AU  - Guo, Jing
AU  - Li, Xiaoxue
TI  - On the $k$-polygonal numbers and the mean value of Dedekind sums
JO  - Czechoslovak Mathematical Journal
PY  - 2016
SP  - 409
EP  - 415
VL  - 66
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-016-0264-z/
DO  - 10.1007/s10587-016-0264-z
LA  - en
ID  - 10_1007_s10587_016_0264_z
ER  - 
%0 Journal Article
%A Guo, Jing
%A Li, Xiaoxue
%T On the $k$-polygonal numbers and the mean value of Dedekind sums
%J Czechoslovak Mathematical Journal
%D 2016
%P 409-415
%V 66
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-016-0264-z/
%R 10.1007/s10587-016-0264-z
%G en
%F 10_1007_s10587_016_0264_z
Guo, Jing; Li, Xiaoxue. On the $k$-polygonal numbers and the mean value of Dedekind sums. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 409-415. doi: 10.1007/s10587-016-0264-z

Cité par Sources :