Geodesic
On a ternary Diophantine problem with mixed powers of primes
Alessandro Languasco1 ; Alessandro Zaccagnini2
1 Dipartimento di Matematica Università di Padova Via Trieste 63 35121 Padova, Italy
2 Dipartimento di Matematica e Informatica Università di Parma Parco Area delle Scienze 53/a 43124 Parma, Italy
Acta Arithmetica, Tome 159 (2013) no. 4, pp. 345-362.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 such that $\lambda_1 / \lambda_2$ is irrational, and $\varpi$ is any real number, then for any $\varepsilon > 0$ the inequality $\vert\lambda_1 p_1 + \lambda_2 p_2^2 + \lambda_3 p_3^k +\varpi\vert \le( \max_j p_j )^{-(33 - 29 k) / (72 k) + \varepsilon}$ has infinitely many solutions in prime variables $p_1$, $p_2$, $p_3$.
DOI : 10.4064/aa159-4-4
Keywords: prove lambda lambda lambda non zero real numbers sign lambda lambda irrational varpi real number varepsilon inequality vert lambda lambda lambda varpi vert max varepsilon has infinitely many solutions prime variables

Alessandro Languasco 1 ; Alessandro Zaccagnini 2

1 Dipartimento di Matematica Università di Padova Via Trieste 63 35121 Padova, Italy
2 Dipartimento di Matematica e Informatica Università di Parma Parco Area delle Scienze 53/a 43124 Parma, Italy 
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Alessandro Languasco; Alessandro Zaccagnini. On a ternary Diophantine problem with
 mixed powers of primes. Acta Arithmetica, Tome 159 (2013) no. 4, pp. 345-362. doi : 10.4064/aa159-4-4. http://geodesic.mathdoc.fr/articles/10.4064/aa159-4-4/

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