Vinogradov’s theorem with Fouvry–Iwaniec primes

Lasse Grimmelt

Type: Article

Publication Date: 2022-10-16

Citations: 5

DOI: https://doi.org/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.

Locations

Algebra & Number Theory - View
arXiv (Cornell University) - View - PDF

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+ PDF Chat	A transference principle for systems of linear equations, and applications to almost twin primes	2023	Pierre‐Yves Bienvenu Xuancheng Shao Joni Teräväinen
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Works Cited by This (31)

Action	Title	Year	Authors
+ PDF Chat	Primes of the type φ(x, y)+A where φ is a quadratic form	1972	Henryk Iwaniec
+	A Brun-Titschmarsh theorem for multiplicative functions.	1980	Peter Shiu
+	ON THE REPRESENTATION OF A LARGER EVEN INTEGER AS THE SUM OF A PRIME AND THE PRODUCT OF AT MOST TWO PRIMES	1973	Chen Jing-Run
+	Opera de Cribro	2010	John Friedlander Henryk Iwaniec
+	Analytic Methods for Diophantine Equations and Diophantine Inequalities	2005	H. Davenport T. D. Browning
+ PDF Chat	Lectures on the geometry of numbers	1990	K. Chandrasekharan
+ PDF Chat	Integers free of small prime factors in arithmetic progressions	2000	Ti Xuan
+	The ternary Goldbach conjecture is true	2013	H. A. Helfgott
+ PDF Chat	On the switching principle in sieve theory.	1986	Étienne Fouvry Frieder Grupp
+	On Λ(p)-subsets of squares	1989	Jean Bourgain