Vinogradov's Theorem with Fouvry-Iwaniec Primes

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.

arXiv comment60 pages. Updated version corrects several minor issues of original paper. To appear in Algebra and Number Theory

References in corpus (6)

• The ternary Goldbach conjecture is true
• A Density Version of the Vinogradov Three Primes Theorem
• Vinogradov's theorem with almost equal summands
• Vinogradov's three primes theorem with almost twin primes
• Minor arcs, mean values, and restriction theory for exponential sums over smooth numbers
• The Goldbach Problem for Primes That Are Sums of Two Squares Plus One

Cited by in corpus (2)

• On prime values of binary quadratic forms with a thin variable
• A transference principle for systems of linear equations, and applications to almost twin primes