Volume no :18, Issue no: 1, September-December (2017)

TWO ELEMENTARY FORMULAE AND SOME COMPLICATED PROPERTIES FOR MERTENS FUNCTION

Author's: Rong Qiang Wei
Pages: [15] - [33]
Received Date: November 13, 2017
Submitted by:
DOI: http://dx.doi.org/10.18642/jantaa_7100121887

Abstract

Two elementary formulae for Mertens function are obtained. With these formulae, can be calculated directly and simply, which can be easily implemented by computer. are calculated one by one. Based on these samples, some of the complicated properties for Mertens function its 16479 zeros, the 10043 local maximum/minimum between two neighbour zeros, and the relation with the cumulative sum of the squarefree integers, are understood numerically and empirically.

Keywords

Mertens function, elementary formula, zeros, local maximum/ minimum, squarefree integers.