Constant Components of the Mertens Function and Its Connections with Tschebyschef’s Theory for Counting Prime Numbers

Autor:	Paulo Agozzini Martin, André Pierro de Camargo
Rok vydání:	2021
Předmět:	Combinatorics Alternating series Mertens function General Mathematics Prime number TEORIA ANALÍTICA DOS NÚMEROS Function (mathematics) Constant (mathematics) Möbius function Prime (order theory) Mathematics
Zdroj:	Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP
ISSN:	1678-7714 1678-7544
Popis:	In this note we exhibit some large sets $$\varTheta _x \subset \{1, 2, \ldots , \lfloor x \rfloor \}$$ such that the sum of the Mobius function over $$\varTheta _x$$ is small and independent of x. We show that the existence of some of these sets are intimately connected with the existence of the alternating series used by Tschebyschef and Sylvester to bound the prime counter function $$\varPi (x)$$ .
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1ba4d3a47a12932e6a20ae9b3d7d178a https://doi.org/10.1007/s00574-021-00267-4 Zobrazit plný text záznamu Full text from SpringerLink