Notes de lecture de l'article "Partial sums of the Möbius function" de Kannan Soundararajan

2008/10/20 by Michel Balazard, Balazard, Michel, Anne De Roton +1
Mathematics · #11M26 #11N37 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M26 #msc:11N37

paper · pdf · doi:10.48550/arxiv.0810.3587

25 pages

arxiv created 2008/10/20 · arxiv updated 2009/12/01

Abstract

Kannan Soundararajan recently obtained a new estimate, conditional to the Riemann hypothesis, for the summatory function of the Mobius function. In this expository article we describe his method, with detailed computations.

Related

• Estimates of sums related to the Nyman-Beurling criterion for the Riemann Hypothesis
• Partial sums of the Möbius function in arithmetic progressions assuming GRH
• Conversions explicites entre des fonctions sommatoires de la fonction de Möbius
• The distribution of the summatory function of the Möbius function
• Explicit estimates of sums related to the Nyman-Beurling criterion for the Riemann Hypothesis