Vinogradov’s theorem with Fouvry–Iwaniec primes

Grimmelt, Lasse

doi:10.2140/ant.2022.16.1705

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Vinogradov's theorem with Fouvry–Iwaniec primes

Lasse Grimmelt

Vol. 16 (2022), No. 7, 1705–1776

DOI: 10.2140/ant.2022.16.1705

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. 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

Milestones

Received: 10 March 2021

Revised: 2 September 2021

Accepted: 5 October 2021

Published: 16 October 2022

Authors

Lasse Grimmelt
University of Oxford Oxford United Kingdom

Vol. 16, No. 7, 2022