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- Title
Results of Diophantine approximation by unlike powers of primes.
- Authors
Gao, Gaiyun; Liu, Zhixin
- Abstract
Let k be an integer with k ≥ 6: Suppose that λ1, λ2,..., λ5 be nonzero real numbers not all of the same sign, satisfying that λ1/λ2 is irrational, and suppose that η is a real number. In this paper, for any ε > 0; we consider the inequality |λ1p1 + λ2p22 + λ3p33 + λ4p44 + λ5p5k + η | < (max pj)-σ(k)+ε has infinitely many solutions in prime variables p1, p2,...,p5, where σ(k) depends on k. 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.
- Subjects
DIOPHANTINE analysis; INTEGERS; REAL numbers; IRRATIONAL numbers; INFINITE element method
- Publication
Frontiers of Mathematics in China, 2018, Vol 13, Issue 4, p797
- ISSN
1673-3452
- Publication type
Article
- DOI
10.1007/s11464-018-0713-0