Primes in the intersection of two Piatetski-Shapiro sets

2023/09/12 by Li, Xiaotian, Zhai, Wenguang, Li, Jinjiang · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2309.06026

Abstract

Let π(x;γ1,γ2) denote the number of primes p with p\leqslant x and p=\lfloor n1/γ11\rfloor=\lfloor n1/γ22\rfloor, where \lfloor t\rfloor denotes the integer part of t∈ℝ and 1/2<γ2<γ1<1 are fixed constants. In this paper, we show that π(x;γ1,γ2) holds an asymptotic formula for 21/11<γ1+γ2<2, which constitutes an improvement upon the previous result of Baker [1].

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• Vinogradov's three primes theorem in the intersection of multiple Piatetski-Shapiro sets

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