Representation of an integer as the sum of a prime in arithmetic progression and a squarefree integer with certain parity

Kam Hung Yau

Published 2019-04-14Version 1

Uniformly for small $q$ and $(a,q)=1$, we obtain an estimate for the weighted number of ways a sufficiently large integer can be represented as the sum of a prime congruent to $a$ modulo $q$ and a squarefree integer with an even (or odd) number of prime factors. Our method is based on the notion of local model developed by Ramar\'e and may be viewed as an abstract circle method.