Multiplicative functions supported on the k-free integers with small partial sums

被引：0

作者：

Aymone, Marco ^{[1
]}

Bueno, Caio ^{[1
]}

Medeiros, Kevin ^{[1
]}

机构：

[1] Univ Fed Minas Gerais UFMG, Dept Matemat, Av Antonio Carlos 6627,Caixa Postal 702, BR-31270901 Belo Horizonte, MG, Brazil

来源：

RAMANUJAN JOURNAL | 2022年 / 59卷 / 03期

关键词：

Multiplicative functions; k-Free integers; Generalized Riemann hypothesis;

D O I：

10.1007/s11139-022-00618-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide examples of multiplicative functions f supported on the k-free integers such that at primes f (p) = +/- 1 and such that the partial sums of f up to x are o(x(1/k)). Further, if we assume the Generalized Riemann Hypothesis, then we can improve the exponent 1/k: There are examples such that the partial sums up to x are o(x(1/(k+ 1/2)+epsilon)), for all epsilon > 0. This generalizes to the k-free integers the results of Aymone.

引用

页码：713 / 728

页数：16

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