On the $k$-polygonal numbers and the mean value of Dedekind sums

Guo, Jing, and Li, Xiaoxue. "On the $k$-polygonal numbers and the mean value of Dedekind sums." Czechoslovak Mathematical Journal 66.2 (2016): 409-415. <http://eudml.org/doc/280101>.

@article{Guo2016,
abstract = {For any positive integer $k\ge 3$, it is easy to prove that the $k$-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 $L$-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 $k$-polygonal numbers with $1\le m,n\le p-1$, and give an interesting computational formula for it.},
author = {Guo, Jing, Li, Xiaoxue},
journal = {Czechoslovak Mathematical Journal},
keywords = {Dedekind sums; mean value; computational problem; $k$-polygonal number; analytic method},
language = {eng},
number = {2},
pages = {409-415},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the $k$-polygonal numbers and the mean value of Dedekind sums},
url = {http://eudml.org/doc/280101},
volume = {66},
year = {2016},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 409
EP - 415
AB - For any positive integer $k\ge 3$, it is easy to prove that the $k$-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 $L$-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 $k$-polygonal numbers with $1\le m,n\le p-1$, and give an interesting computational formula for it.
LA - eng
KW - Dedekind sums; mean value; computational problem; $k$-polygonal number; analytic method
UR - http://eudml.org/doc/280101
ER -