| Title:
|
On the $k$-polygonal numbers and the mean value of Dedekind sums (English) |
| Author:
|
Guo, Jing |
| Author:
|
Li, Xiaoxue |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
409-415 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Dedekind sums |
| Keyword:
|
mean value |
| Keyword:
|
computational problem |
| Keyword:
|
$k$-polygonal number |
| Keyword:
|
analytic method |
| MSC:
|
11L05 |
| MSC:
|
11L10 |
| idZBL:
|
Zbl 06604475 |
| idMR:
|
MR3519610 |
| DOI:
|
10.1007/s10587-016-0264-z |
| . |
| Date available:
|
2016-06-16T12:49:11Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145732 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| . |
