Diophantine inequalities over Piatetski-Shapiro primes

Abstract

Let c>1 and : We study the solubility of the Diophantine inequality in Piatetski-Shapiro primes p₁,p₂, .., p_s of the form p_j=[m^{\gamma }] for some m\in \mathbb{N}, and improve the previous results in the cases s = 2, 3, 4.

Keywords

Diophantine inequalities / Piatetski-Shapiro primes / exponential sums / additive problems

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