On a ternary Diophantine problem with mixed powers of primes

Alessandro Languasco, and Alessandro Zaccagnini. "On a ternary Diophantine problem with mixed powers of primes." Acta Arithmetica 159.4 (2013): 345-362. <http://eudml.org/doc/279470>.

@article{AlessandroLanguasco2013,
abstract = {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.},
author = {Alessandro Languasco, Alessandro Zaccagnini},
journal = {Acta Arithmetica},
keywords = {Diophantine problems with primes; primes in short intervals},
language = {eng},
number = {4},
pages = {345-362},
title = {On a ternary Diophantine problem with mixed powers of primes},
url = {http://eudml.org/doc/279470},
volume = {159},
year = {2013},
}

TY - JOUR
AU - Alessandro Languasco
AU - Alessandro Zaccagnini
TI - On a ternary Diophantine problem with mixed powers of primes
JO - Acta Arithmetica
PY - 2013
VL - 159
IS - 4
SP - 345
EP - 362
AB - 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.
LA - eng
KW - Diophantine problems with primes; primes in short intervals
UR - http://eudml.org/doc/279470
ER -