Diophantine approximation over primes with different powers

Huafeng Liu and Jun Yue

Applied Mathematics and Computation, 2022, vol. 421, issue C

Abstract: Assume non-zero real numbers κ1,…,κ6 are not all negative. Assume also κ1κ2 is algebraic and not rational, the sequence G is well-spaced and ϑ>0. In this work, we showed that the quantity of γ∈G satisfying 1≤γ≤X and making the Diophantine inequality|κ1p12+κ2p22+κ3p33+κ4p43+κ5p54+κ6p64−γ|<γ−ϑunsolvable in primes p1,…,p6 is not more than O(X67+2ϑ+ϵ) for any ϵ>0.

Keywords: Diophantine approximation; Sieve function; Prime (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000261

DOI: 10.1016/j.amc.2022.126940

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