| Title:
|
Some new sums related to D. H. Lehmer problem (English) |
| Author:
|
Zhang, Han |
| Author:
|
Zhang, Wenpeng |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
915-922 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Lehmer number |
| Keyword:
|
analytic method |
| Keyword:
|
trigonometric sums |
| Keyword:
|
asymptotic formula |
| MSC:
|
11L05 |
| MSC:
|
11L40 |
| idZBL:
|
Zbl 06537700 |
| idMR:
|
MR3441325 |
| DOI:
|
10.1007/s10587-015-0217-y |
| . |
| Date available:
|
2016-01-13T09:04:38Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144782 |
| . |
| 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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| . |
