The distribution of the summatory function of the Möbius function

• Autores: Nathan Ng
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 89, Nº 2, 2004, págs. 361-389
• Idioma: inglés
• DOI: 10.1112/s0024611504014741
• Texto completo no disponible (Saber más ...)
• Resumen

  • The summatory function of the Möbius function is denoted $M(x)$. In this article we deduce conditional results concerning $M(x)$ assuming the Riemann hypothesis and a conjecture of Gonek and Hejhal on the negative moments of the Riemann zeta function. Assuming these conjectures, we show that $M(x)$, when appropriately normalized, possesses a limiting distribution, and also that a strong form of the weak Mertens conjecture is true. Finally, we speculate on the lower order of $M(x)$ by studying the constructed distribution function.