Let \$1&lt;14/5\$, \$lambda_1,lambda_2,lambda_3\$ and \$lambda_4\$ be non-zero real numbers, not all of the same sign such that \$lambda_1/lambda_2\$ is irrational and let \$omega\$ be a real number. We prove that the inequality \$|lambda_1p_1+lambda_2p_2^2+lambda_3p_3^2+lambda_4p_4^k-omega|le (max (p_1,p_2^2,p_3^2,p_4^k))^{-psi(k)+arepsilon}\$ has infinitely many solutions in prime variables \$p_1,p_2,p_3,p_4\$ for any \$arepsilon&gt;0\$ where \$psi(k)=minleft(rac1{14},rac{14-5k}{28k} ight)\$.

Diophantine approximation with one prime, two squares of primes and one kth power of a prime / Gambini, A.. - In: OPEN MATHEMATICS. - ISSN 2391-5455. - 19:1(2021), pp. 373-387. [10.1515/math-2021-0044]

Diophantine approximation with one prime, two squares of primes and one kth power of a prime

Abstract

Let \$1<14/5\$, \$lambda_1,lambda_2,lambda_3\$ and \$lambda_4\$ be non-zero real numbers, not all of the same sign such that \$lambda_1/lambda_2\$ is irrational and let \$omega\$ be a real number. We prove that the inequality \$|lambda_1p_1+lambda_2p_2^2+lambda_3p_3^2+lambda_4p_4^k-omega|le (max (p_1,p_2^2,p_3^2,p_4^k))^{-psi(k)+arepsilon}\$ has infinitely many solutions in prime variables \$p_1,p_2,p_3,p_4\$ for any \$arepsilon>0\$ where \$psi(k)=minleft(rac1{14},rac{14-5k}{28k} ight)\$.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11573/1598994`
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