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.
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.
Keywords: Quadratic uniformity, Möbius function
Mot clés : uniformité quadratique, fonction de Möbius
@article{AIF_2008__58_6_1863_0, author = {Green, Ben and Tao, Terence}, title = {Quadratic uniformity of the {M\"obius} function}, journal = {Annales de l'Institut Fourier}, pages = {1863--1935}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {6}, year = {2008}, doi = {10.5802/aif.2401}, zbl = {1160.11017}, mrnumber = {2473624}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2401/} }
TY - JOUR AU - Green, Ben AU - Tao, Terence TI - Quadratic uniformity of the Möbius function JO - Annales de l'Institut Fourier PY - 2008 SP - 1863 EP - 1935 VL - 58 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2401/ DO - 10.5802/aif.2401 LA - en ID - AIF_2008__58_6_1863_0 ER -
%0 Journal Article %A Green, Ben %A Tao, Terence %T Quadratic uniformity of the Möbius function %J Annales de l'Institut Fourier %D 2008 %P 1863-1935 %V 58 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2401/ %R 10.5802/aif.2401 %G en %F AIF_2008__58_6_1863_0
Green, Ben; Tao, Terence. Quadratic uniformity of the Möbius function. Annales de l'Institut Fourier, Volume 58 (2008) no. 6, pp. 1863-1935. doi : 10.5802/aif.2401. http://archive.numdam.org/articles/10.5802/aif.2401/
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