| Title:
|
Sidon basis in polynomial rings over finite fields (English) |
| Author:
|
Kuo, Wentang |
| Author:
|
Yamagishi, Shuntaro |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
555-562 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\mathbb {F}_q[t]$ denote the polynomial ring over $\mathbb {F}_q$, the finite field of $q$ elements. Suppose the characteristic of $\mathbb {F}_q$ is not $2$ or $3$. We prove that there exist infinitely many $N \in \mathbb {N}$ such that the set $\{ f \in \mathbb {F}_q[t] \colon \deg f < N \}$ contains a Sidon set which is an additive basis of order $3$. (English) |
| Keyword:
|
Sidon set |
| Keyword:
|
additive basis |
| Keyword:
|
polynomial rings over finite fields |
| MSC:
|
11B83 |
| MSC:
|
11K31 |
| MSC:
|
11T55 |
| idZBL:
|
07361085 |
| idMR:
|
MR4263186 |
| DOI:
|
10.21136/CMJ.2020.0543-19 |
| . |
| Date available:
|
2021-05-20T13:47:33Z |
| Last updated:
|
2023-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148921 |
| . |
| 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:
|
[8] Kiss, S. Z., Rozgonyi, E., Sándor, C.: On Sidon sets which are asymptotic bases of order 4.Funct. Approximatio, Comment. Math. 51 (2014), 393-413. Zbl 1353.11016, MR 3282635, 10.7169/facm/2014.51.2.10 |
| Reference:
|
[9] Konyagin, S. V., Lev, V. F.: The Erdős-Turán problem in infinite groups.Additive Number Theory Springer, New York (2010), 195-202. Zbl 1271.11011, MR 2744757, 10.1007/978-0-387-68361-4_14 |
| Reference:
|
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| Reference:
|
[11] O'Bryant, K.: A complete annotated bibliography of work related to Sidon sequences.Electron. J. Comb. DS11 (2004), 39 pages. Zbl 1142.11312 |
| . |
