A Variant of Mobius Inversion

被引：1
|
作者：
Cardinal, Jean-Paul [1 ]
Overholt, Marius [2 ]
机构：
[1] Univ Paris 13, Dept Math, Inst Galilee, 99 Ave Jean Baptiste Clement, Villetaneuse, France
[2] Univ Tromso, Dept Math & Stat, NO-9037 Tromso, Norway
来源：
EXPERIMENTAL MATHEMATICS | 2020年 / 29卷 / 03期
关键词：
Mertens function; Riemann hypothesis; Mobius inversion; divisor matrix;
D O I：
10.1080/10586458.2018.1459960
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We develop a new approach to Mobius inversion by considering the spectral problem for certain symmetric, positive-definite matrices closely connected to the divisibility relation. This spectral problem appears to have significance for analytic number theory. We obtain a novel version of the second Mobius inversion formula, and in particular a new formula for the Mertens function. Computational evidence regarding the latter formula may throw some light on the Riemann Hypothesis.
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页码：247 / 252
页数：6
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