Quadratic uniformity of the Möbius function
[L’uniformité quadratique de la fonction de Möbius]
Green, Ben1 ; Tao, Terence2
1 Centre for Mathematical Sciences Wilberforce Road Cambridge CB3 0WA (England)
2 UCLA Department of Mathematics Los Angeles CA 90095-1596 (USA)
Annales de l'Institut Fourier, Tome 58 (2008) no. 6, pp. 1863-1935.

On établit la conjecture « Möbius et Nilsuites » pour les nilsystèmes de rang 1 et 2. Ce papier est une partie de notre programme, dont le but est une généralisation de la méthode de Hardy-Littlewood en vue d’étudier les systèmes d’équations linéaires dans les nombres premiers.

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.

DOI : 10.5802/aif.2401
Classification : 11B99
Keywords: Quadratic uniformity, Möbius function
Mot clés : uniformité quadratique, fonction de Möbius
Green, Ben 1 ; Tao, Terence 2

1 Centre for Mathematical Sciences Wilberforce Road Cambridge CB3 0WA (England)
2 UCLA Department of Mathematics Los Angeles CA 90095-1596 (USA) 
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Green, Ben; Tao, Terence. Quadratic uniformity of the Möbius function. Annales de l'Institut Fourier, Tome 58 (2008) no. 6, pp. 1863-1935. doi : 10.5802/aif.2401. http://www.numdam.org/articles/10.5802/aif.2401/

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