PROBABILISTIC PROOF OF THE MEAN-VALUE THEOREM FOR [0,<i> </i>1]-VALUED MULTIPLICATIVE FUNCTIONS BY MEANS OF THE ADELIC FORMULATION

IF 0.6 4区数学 Q3 MATHEMATICS

Kyushu Journal of Mathematics Pub Date : 2023-01-01 DOI:10.2206/kyushujm.77.355

Hiroshi SUGITA

引用次数: 0

Abstract

A probabilistic proof by means of the adelic formulation is given to the classical mean-value theorem for [0, 1]-valued multiplicative arithmetical functions f. Then a more general mean-value theorem is derived for composite functions φ(f) of f with (semi-)continuous functions φ.

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[0，<i>]中值定理的概率证明</i>1]用阿德利克公式求解多值乘法函数

利用阿得利克公式给出了[0,1]值乘性算术函数f的经典中值定理的概率证明，然后导出了f的复合函数φ(f)与(半)连续函数φ的更一般的中值定理。

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

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.