Quadratic uniformity of the Möbius function

Ben Green, Terence Tao

Type: Article

Publication Date: 2008-01-01

Citations: 51

DOI: https://doi.org/10.5802/aif.2401

Abstract

We prove the "Möbius and Nilsequences Conjecture" for nilsystems of step 1 and 2. This paper forms a part of our program to generalise the Hardy-Littlewood method so as to handle systems of linear equations in primes.

Locations

Annales de l’institut Fourier - View - PDF
arXiv (Cornell University) - View - PDF
arXiv (Cornell University) - View - PDF
arXiv (Cornell University) - PDF
Annales de l’institut Fourier - View - PDF
arXiv (Cornell University) - View - PDF
arXiv (Cornell University) - View - PDF
arXiv (Cornell University) - PDF

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+ PDF	AN INVERSE THEOREM FOR THE GOWERS<i>U</i><sup>4</sup>-NORM	2010	Ben Green Terence Tao Tamar Ziegler
+ PDF	Sets of integers with no large sum-free subset	2014	Sean Eberhard Ben Green Freddie Manners
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Works Cited by This (22)

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+	Handbuch der Lehre von der Verteilung der Primzahlen	1911	Edmund Landau
+	Representations of nilpotent Lie groups and their applications	1989	Lawrence Corwin Frederick Greenleaf
+	Arithmetic progressions and the primes	2006	Terence Tao
+	ON SOME INFINITE SERIES INVOLVING ARITHMETICAL FUNCTIONS (II)	1937	H. Davenport
+	Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis	1994	Hugh L. Montgomery
+	SOME RESULTS IN THE ADDITIVE PRIME-NUMBER THEORY	1938	Loo-Keng Hua
+	Finite field models in additive combinatorics	2005	Ben Green
+ PDF	Linear equations in primes	2010	Ben Green Terence Tao
+	Über Summen von Primzahlen und Primzahlquadraten	1939	J. G. van der Corput
+	Linear equations in primes	1992	Antal Balog