On the estimate \(M(x)=o(x)\) for Beurling generalized numbers

IF 0.6 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2024-10-29 DOI:10.1007/s10476-024-00061-6

J. Vindas

引用次数: 0

Abstract

We show that the sum function of the Möbius function of a Beurling number system must satisfy the asymptotic bound \(M(x)=o(x)\) if it satisfies the prime number theorem and its prime distribution function arises from a monotone perturbation of either the classical prime numbers or the logarithmic integral.

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关于Beurling广义数的估计\(M(x)=o(x)\)

我们证明了一个Beurling数系统的Möbius函数的和函数必须满足渐近界\(M(x)=o(x)\)，如果它满足素数定理，并且它的素数分布函数是由经典素数或对数积分的单调扰动引起的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.