A hybrid of two theorems of Piatetski-Shapiro

2018/03/11 by Kumchev, Angel, Petrov, Zhivko
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1803.03952

Abstract

Let c > 1 and 0 < γ< 1 be real, with c ∉ \mathbb N. We study the solubility of the Diophantine inequality | p₁^c + p₂^c + … + p_s^c - N | lt; ε in Piatetski-Shapiro primes p₁, p₂, …, p_s of index γ---that is, primes of the form p = \lfloor m^1/γ \rfloor for some m ∈ \mathbb N.

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