在线咨询
中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (3): 340-354.doi: 10.3969/j.issn.1005-3085.2018.03.009

• • 上一篇    下一篇

一类数论函数的刻画（英）

尤利华,   陈亚菲,   袁平之,   沈洁琴   

  1. 华南师范大学数学与科学学院，广州  510631
  • 收稿日期:2016-09-04 接受日期:2017-09-12 出版日期:2018-06-15 发布日期:2018-08-15
  • 基金资助:
    国家自然科学基金(11571123;11271142)；广东省自然科学基金(2015A030313377)；华南师范大学研究生院科研基金(2015lkxm19).

A Characterization of a Class of Arithmetic Functions

YOU Li-hua,   CHEN Ya-fei,    YUAN Ping-zhi,   SHEN Jie-qin   

  1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631
  • Received:2016-09-04 Accepted:2017-09-12 Online:2018-06-15 Published:2018-08-15
  • Supported by:
    The National Natural Science Foundation of China (11571123; 11271142); the Guangdong Provincial Natural Science Foundation (2015A030313377); the Scientific Research Foundation of Graduate School of South China Normal University (2015lkxm19).

PDF (PC)

236

摘要： 近二十年来，关于正整数的Cauchy型函数方程已经有大量的研究工作．众所周知，数论函数在人工智能、密码学以及工程等领域都有着更广泛的应用．该文主要研究一类数论函数的刻画．首先，我们给出了该类数论函数在给定条件下的刻画并证明，进而得到一个猜想并证明了该猜想在若干简单的情形下成立．最后，我们总结证明过程并指出了若干个有趣的小发现．

关键词: 数论函数, 函数方程, 刻画

Abstract: During the last decade, there have been a great deal of researches on Cauchy-like functional equation on positive integer. As we know, the arithmetic function is widely applied in the field of artificial intelligence, cryptography and engineering. This paper mainly discusses the characterization of a class of arithmetic functions. Firstly, we give a characterization under some condition, and then propose a conjecture and show that the result holds for several simple cases. Finally, we summarize the process of argument and give some valuable conclusions which have been found during the proof process.

Key words: arithmetic function, functional equation, characterization

中图分类号: