A Vinogradov-type problem in almost primes

Abstract

We prove a generalisation of Vinogradov's theorem by finding for $m⩾3$ and fixed positive integers $c_1,\dots ,c_m,r_1,\dots ,r_m$ the asymptotics of the number of sequences $(n_1,\dots ,n_m)\in {\mathbf{N}}^m$ such that $c_1{n}_1+\cdots +c_m{n}_m=N$ and $\Omega (n_i)=r_i$ for every $i=1,\dots ,m$ under the assumption that at least three of the $r_i$ are equal to $1$.

21 pages

References in corpus (1)

• Minor arcs for Goldbach's problem