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.

引用

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页码：247 / 252

页数：6

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