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Vinogradov's theorem with Fouvry–Iwaniec primes

Lasse Grimmelt

Vol. 16 (2022), No. 7, 1705–1776

We show that every sufficiently large x 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.

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Goldbach-type theorems, transference principle
Mathematical Subject Classification
Primary: 11N36, 11P32
Received: 10 March 2021
Revised: 2 September 2021
Accepted: 5 October 2021
Published: 16 October 2022
Lasse Grimmelt
University of Oxford
United Kingdom