| Title:
|
The exceptional set for Diophantine inequality with unlike powers of prime variables (English) |
| Author:
|
Ge, Wenxu |
| Author:
|
Zhao, Feng |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
149-168 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Suppose that $\lambda _1,\lambda _2,\lambda _3,\lambda _4$ are nonzero real numbers, not all negative, $\delta > 0$, $\mathcal {V}$ is a well-spaced set, and the ratio $\lambda _1/\lambda _2$ is algebraic and irrational. Denote by $E(\mathcal {V}, N,\delta )$ the number of $v\in \mathcal {V}$ with $v\leq N$ such that the inequality $$ |\lambda _1p_1^2+\lambda _2p_2^3+\lambda _3p_3^4+\lambda _4p_4^5-v|<v^{-\delta } $$ has no solution in primes $p_1$, $p_2$, $p_3$, $p_4$. We show that $$ E(\mathcal {V}, N,\delta )\ll N^{1+2\delta -{1}/{72}+\varepsilon } $$ for any $\varepsilon >0$. (English) |
| Keyword:
|
Davenport-Heilbronn method |
| Keyword:
|
prime varaible |
| Keyword:
|
exceptional set |
| Keyword:
|
Diophantine inequality |
| MSC:
|
11D75 |
| MSC:
|
11P32 |
| MSC:
|
11P55 |
| idZBL:
|
Zbl 06861573 |
| idMR:
|
MR3783591 |
| DOI:
|
10.21136/CMJ.2018.0388-16 |
| . |
| Date available:
|
2018-03-19T10:27:59Z |
| Last updated:
|
2020-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147127 |
| . |
| Reference:
|
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