Almost sure bounds for a weighted Steinhaus random multiplicative function

IF 1 2区数学 Q1 MATHEMATICS Journal of the London Mathematical Society-Second Series Pub Date : 2024-08-22 DOI:10.1112/jlms.12979

Seth Hardy

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Abstract

We obtain almost sure bounds for the weighted sum $\sum_{n ⩽ t} \frac{f (n)}{\sqrt{n}}$ , where $f (n)$ is a Steinhaus random multiplicative function. Specifically, we obtain the bounds predicted by exponentiating the law of the iterated logarithm, giving sharp upper and lower bounds.

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加权斯坦豪斯随机乘法函数的几乎确定边界

我们得到了加权和 ∑ n ⩽ t f ( n ) n $\sum _{n \leqslant t} 的几乎确定的边界。\其中 f ( n ) $f(n)$ 是一个斯坦豪斯随机乘法函数。具体来说，我们通过迭代对数的指数化法则得到了预测的边界，给出了尖锐的上下限。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.