A Vinogradov-type problem in almost primes

2016/01/11 by Paweł Lewulis, Lewulis, Paweł
Mathematics · #11P32 #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1601.02591

openalex publication_date 2016/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a generalisation of Vinogradov's theorem by finding for m\geqslant 3 and fixed positive integers c₁, … ,c_m, r₁, … , r_m the asymptotics of the number of sequences (n₁, … ,n_m) ∈ N^m such that c₁n₁ + … + c_m n_m = N and Ω(n_i) = r_i for every i=1, … ,m under the assumption that at least three of the r_i are equal to 1.

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