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Diophantine approximation with two primes and one square of prime. (English) Zbl 1274.11111
Summary: We show that if \(\lambda_1,\lambda_2,\lambda_3\) are non-zero real numbers, not all of them are the same sign, \(\eta\) is real and \(\lambda_1/\lambda_2\) is irrational, then there are infinitely many ordered triples of primes \((p_1, p_2, p_3)\) for which \(|\lambda_1p_1+\lambda_2p_2+\lambda_3p_3^2+\eta|<(\max p_j)^{-\frac 1{40}}(\log \max p_j)^4\).

MSC:
11J25 Diophantine inequalities
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