Let $1 < k < 33 / 29$. We prove that if $\lambda_1$, $\lambda_2$ and $\lambda_3$ are non-zero real numbers, not all of the same sign and that $\lambda_1 / \lambda_2$ is irrational and $\varpi$ is any real number then, for any $\eps > 0$ the inequality $ \bigl\vert \lambda_1 p_1 + \lambda_2 p_2^2 + \lambda_3 p_3^k + \varpi \bigr\vert \le \bigl( \max_j p_j \bigr)^{-(33 - 29 k) / (72 k) + \eps} $ has infinitely many solution in prime variables $p_1$, \dots, $p_3$.
On a ternary Diophantine problem with mixed powers of primes
LANGUASCO, ALESSANDRO;
2013
Abstract
Let $1 < k < 33 / 29$. We prove that if $\lambda_1$, $\lambda_2$ and $\lambda_3$ are non-zero real numbers, not all of the same sign and that $\lambda_1 / \lambda_2$ is irrational and $\varpi$ is any real number then, for any $\eps > 0$ the inequality $ \bigl\vert \lambda_1 p_1 + \lambda_2 p_2^2 + \lambda_3 p_3^k + \varpi \bigr\vert \le \bigl( \max_j p_j \bigr)^{-(33 - 29 k) / (72 k) + \eps} $ has infinitely many solution in prime variables $p_1$, \dots, $p_3$.File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
