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On Diophantine approximation by unlike powers of primes
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ge, Wenxu Li, Weiping Wang, Tianze |
| Copyright Year | 2019 |
| Abstract | Abstract Suppose that λ1, λ2, λ3, λ4, λ5 are nonzero real numbers, not all of the same sign, λ1/λ2 is irrational, λ2/λ4 and λ3/λ5 are rational. Let η real, and ε > 0. Then there are infinitely many solutions in primes pj to the inequality |λ1p1+λ2p22+λ3p33+λ4p44+λ5p55+η|<(maxpjj)−1/32+ε $\begin{array}{} \displaystyle |\lambda_1p_1+\lambda_2p_2^2+\lambda_3p_3^3+\lambda_4p_4^4+\lambda_5p_5^5+\eta| \lt (\max{p_j^j})^{-1/32+\varepsilon} \end{array}$. This improves an earlier result under extra conditions of λj. |
| Starting Page | 544 |
| Ending Page | 555 |
| Page Count | 12 |
| File Format | PDF HTM / HTML |
| DOI | 10.1515/math-2019-0045 |
| Volume Number | 17 |
| Alternate Webpage(s) | https://www.degruyter.com/downloadpdf/j/math.2019.17.issue-1/math-2019-0045/math-2019-0045.pdf |
| Alternate Webpage(s) | https://doi.org/10.1515/math-2019-0045 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |