| Title:
|
On the Waring-Goldbach problem for one square and five cubes in short intervals (English) |
| Author:
|
Xue, Fei |
| Author:
|
Zhang, Min |
| Author:
|
Li, Jinjiang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
563-589 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $N$ be a sufficiently large integer. We prove that almost all sufficiently large even integers $n\in [N-6U,N+6U]$ can be represented as $$ n=p_1^2+p_2^3+p_3^3+p_4^3+p_5^3+p_6^3, \Bigl | p_1^2-\dfrac {N}{6}\Bigr | \leq U, \quad \Bigl | p_i^3-\dfrac {N}{6}\Bigr |\leq U, \quad i=2,3,4,5,6, $$ where $U=N^{1-\delta +\varepsilon }$ with $\delta \leq 8/225$. (English) |
| Keyword:
|
Waring-Goldbach problem |
| Keyword:
|
Hardy-Littlewood method |
| Keyword:
|
exponential sum |
| Keyword:
|
short interval |
| MSC:
|
11P05 |
| MSC:
|
11P32 |
| MSC:
|
11P55 |
| idZBL:
|
07361086 |
| idMR:
|
MR4263187 |
| DOI:
|
10.21136/CMJ.2020.0013-20 |
| . |
| Date available:
|
2021-05-20T13:48:04Z |
| Last updated:
|
2023-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148922 |
| . |
| Reference:
|
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