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 $psi(k)=minleft(rac1{14},rac{14-5k}{28k} ight)$.
Gambini, A. (2021). Diophantine approximation with one prime, two squares of primes and one kth power of a prime. OPEN MATHEMATICS, 19(1), 373-387 [10.1515/math-2021-0044].
Diophantine approximation with one prime, two squares of primes and one kth power of a prime
Gambini A.
2021
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 $psi(k)=minleft(rac1{14},rac{14-5k}{28k} ight)$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
