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### Lasse Grimmelt

Vol. 16 (2022), No. 7, 1705–1776
##### Abstract

We show that every sufficiently large $x\equiv 3\left(4\right)$ can be written as the sum of three primes, each of which is a sum of a square and a prime square. The main tools are a transference version of the circle method and various sieve related ideas. In particular, a majorant of the set of primes of interest is constructed that overestimates it by a factor of less than $3$ and for which we have good control of the Fourier transform.

##### Keywords
Goldbach-type theorems, transference principle
##### Mathematical Subject Classification
Primary: 11N36, 11P32