Almost sure bounds for a weighted Steinhaus random multiplicative function

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-22 DOI:10.1112/jlms.12979

Seth Hardy

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引用次数: 0

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.