On a ternary Diophantine problem with mixed powers of primes

• Autorzy: Alessandro Languasco , Alessandro Zaccagnini
• Języki publikacji: EN

Abstrakty

EN

Let 1 < k < 33/29. We prove that if λ₁, λ₂ and λ₃ are non-zero real numbers, not all of the same sign and such that λ₁/λ₂ is irrational, and ϖ is any real number, then for any ε > 0 the inequality $|λ₁p₁ + λ₂p²₂ + λ₃p₃^k + ϖ | ≤ (max_j p_j)^{-(33-29k)/(72k)+ε}$ has infinitely many solutions in prime variables p₁, p₂, p₃.

Kategorie tematyczne

• 11N05: Distribution of primes
• 11P55: Applications of the Hardy-Littlewood method
• 11D75: Diophantine inequalities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 159
• Numer: 4
• Strony: 345-362

Daty

wydano

2013

Twórcy

autor

Alessandro Languasco

• Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121 Padova, Italy

autor

Alessandro Zaccagnini

• Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/a, 43124 Parma, Italy

Identyfikatory

DOI

10.4064/aa159-4-4