Results of Diophantine approximation by unlike powers of primes
Results of Diophantine approximation by unlike powers of primes
复制标题
DOI：
10.1007/s11464-018-0713-0
复制
发表时间：
2018-07
影响因子：
--
通讯作者：
Gaiyun Gao;Zhixin Liu
中科院分区：
文献类型：
--
作者：
Gaiyun Gao;Zhixin Liu
设k为≥为6的整数：设λ1，λ2，…，λ5为符号不全相同的非零实数，满足λ1/λ2无理，且η为实数。本文对任意ε>；0；考虑了不等式|λ1p1+λ2p22+λ3p33+λ4p44+λ5p5k+η|<；(Maxpj)-σ(K)+ε有无穷多个素变量p1，p2，…，p5的解，其中σ(K)依赖于onk。我们的结果改进了最近的结果。此外，利用本文中类似的方法，我们可以改进不同素数次方逼近丢番图的一些结果，并得到相关问题。
Letkbe an integer withk≥ 6: Suppose that λ1, λ2,..., λ5be nonzero real numbers not all of the same sign, satisfying that λ1/λ2is irrational, and suppose thatηis a real number. In this paper, for anyε> 0; we consider the inequality |λ1p1+ λ2p22+ λ3p33+ λ4p44+ λ5p5k+ η | < (maxpj)-σ(k)+εhas infinitely many solutions in prime variablesp1,p2,...,p5, whereσ(k) depends onk. Our result gives an improvement of the recent result. Furthermore, using the similar method in this paper, we can refine some results on Diophantine approximation by unlike powers of primes, and get the related problem.