Some characterizations of specially multiplicative functions

IF 1 Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-01-01 DOI:10.1155/S0161171203301139

P. Haukkanen

引用次数: 11

Abstract

A multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function fA such that f(m)f(n)=∑d|(m,n)f(mn/d2)fA(d) for all m and n. For example, the divisor functions and Ramanujan's τ-function are specially multiplicative functions. Some characterizations of specially multiplicative functions are given in the literature. In this paper, we provide some further characterizations of specially multiplicative functions.

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特殊乘法函数的一些表征

如果存在一个完全乘法函数fA，使得f(m)f(n)=∑d|(m,n)f(mn/d2)fA(d)对所有m和n都具有特殊的乘法性，那么一个乘法函数f就是特殊的乘法函数。例如，除数函数和拉马努金的τ函数是特殊的乘法函数。在文献中给出了特殊乘法函数的一些表征。本文给出了一些特殊乘法函数的进一步表征。

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

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Mathematics-Mathematics (miscellaneous)

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

17 weeks

期刊介绍： The International Journal of Mathematics and Mathematical Sciences is a refereed math journal devoted to publication of original research articles, research notes, and review articles, with emphasis on contributions to unsolved problems and open questions in mathematics and mathematical sciences. All areas listed on the cover of Mathematical Reviews, such as pure and applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology, are included within the scope of the International Journal of Mathematics and Mathematical Sciences.