素因数之间的一个对偶公式
A Duality Formula between Prime Factors

作者: 杨继明 :玉溪师范学院数学系,云南 玉溪;

关键词: 对偶公式有单位元的交换环素因数反转公式Duality Formula Commutative Ring with Identity Prime Factor Inversion Formula

摘要:

本文把K. Alladi关于素因数之间的一个对偶公式推广到取值在有单位元的交换环的数论函数上,并且得到了若干其他类型的对偶公式。

In this paper we generalize K. Alladi’s duality formula between prime factors to number theoretic functions valued in any commutative ring with identity, and deduce several other kind of duality formulae.

文章引用: 杨继明 (2016) 素因数之间的一个对偶公式。 理论数学, 6, 30-36. doi: 10.12677/PM.2016.61005

参考文献

[1] Liu, H.N. (2004) An Extension of the Möbius Inverse Formula. Journal of Systems Science and Mathematical Sciences, 24, 51-55 (in Chinese).

[2] Xi, P. and Yi, Y. (2009) On Generalized Möbius Inversion Formulae. Acta Mathematica Sinica Sinica, Chinese Series, 52, 1135-1140 (in Chinese).

[3] Yang, J.M. (2014) A Generalization of Möbius Inver-sion Formula. Journal of Baoji University of Arts and Scienses (Natural Science), 34, 1-7 (in Chinese).

[4] Alladi, K. (1977) Duality between Prime Factors and an Application to the Prime Number Theorem for Arithmetic Progressions. Journal of Number Theory, 97, 436-451.
http://dx.doi.org/10.1016/0022-314X(77)90005-1

[5] Kao, J. and Liu, H.N. (2007) A New Duality Formula beween Prime Factors. Mathematics in Practice and Theory, 37, 147-150 (in Chinese).

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