The Distribution of the Summatory Function of the Mobius Function |
| |
Authors: | Ng Nathan |
| |
Affiliation: | Département de Mathématiques et de Statistique, Université de Montréal CP 6128 succursale Centre-Ville, Montréal, Québec H3C 3J7, Canada. E-mail: nathanng{at}dms.umontreal.ca |
| |
Abstract: | The summatory function of the Möbius function is denotedM(x). In this article we deduce conditional results concerningM(x) assuming the Riemann hypothesis and a conjecture of Gonekand Hejhal on the negative moments of the Riemann zeta function.Assuming these conjectures, we show that M(x), when appropriatelynormalized, possesses a limiting distribution, and also thata strong form of the weak Mertens conjecture is true. Finally,we speculate on the lower order of M(x) by studying the constructeddistribution function. 2000 Mathematics Subject Classification11M26, 11N56. |
| |
Keywords: | Mö bius function Riemann zeta function |
本文献已被 Oxford 等数据库收录! |
|