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On a ternary Diophantine problem with mixed powers of primes

Alessandro Languasco, Alessandro Zaccagnini (2013)

Acta Arithmetica

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 | λ p + λ p ² + λ p k + ϖ | ( m a x j p j ) - ( 33 - 29 k ) / ( 72 k ) + ε has infinitely many solutions in prime variables p₁, p₂, p₃.

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