On Diophantine approximation by unlike powers of primes
Copyright policy )On Diophantine approximation by unlike powers of primes
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 $\begin{array}{} \displaystyle |\lambda_1p_1+\lambda_2p_2^2+\lambda_3p_3^3+\lambda_4p_4^4+\lambda_5p_5^5+\eta| \lt (\max{p_j^j})^{-1/32+\varepsilon} \end{array}$. This improves an earlier result under extra conditions of λj.
- Henan University of Economic and Law China (People's Republic of)
- North China University of Water Conservancy and Electric Power China (People's Republic of)
- Hebei University China (People's Republic of)
11d75, Davenport-Heilbronn method, diophantine approximation, davenport-heilbronn method, Applications of the Hardy-Littlewood method, primes, Diophantine inequalities, Diophantine approximation, QA1-939, Goldbach-type theorems; other additive questions involving primes, 11p32, Mathematics, 11p55
11d75, Davenport-Heilbronn method, diophantine approximation, davenport-heilbronn method, Applications of the Hardy-Littlewood method, primes, Diophantine inequalities, Diophantine approximation, QA1-939, Goldbach-type theorems; other additive questions involving primes, 11p32, Mathematics, 11p55
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