Vinogradov's Theorem with Fouvry-Iwaniec Primes

TL;DR

This paper proves that large integers congruent to 3 modulo 4 can be expressed as sums of three special primes, each being a sum of a square and a prime square, using advanced analytic and sieve techniques.

Contribution

Introduces a transference circle method and sieve methods to establish a Vinogradov-type theorem for Fouvry-Iwaniec primes.

Findings

Every sufficiently large x ≡ 3 (4) can be written as a sum of three Fouvry-Iwaniec primes.

Fouvry-Iwaniec primes are sums of a square and a prime square.

The method combines circle method transference with sieve techniques.

Abstract

We show that every sufficiently large $x\equiv 3(4)$ 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.