THE INTEGRATION OF ALGEBROIDAL FUNCTIONS

doi:10.1016/S0252-9602(17)30112-1

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (6): 1861-1869.doi: 10.1016/S0252-9602(17)30112-1

THE INTEGRATION OF ALGEBROIDAL FUNCTIONS

孙道椿¹, 霍颖莹², 孔荫莹³, 柴富杰⁴

1. School of Mathematics, South China Normal University, Guangzhou 510631, China;
2. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China;
3. School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China;
4. Department of Mathematics, Guangzhou Civil Aviation College, Guangzhou 510403, China

收稿日期:2016-02-29 修回日期:2017-05-08 出版日期:2017-12-25 发布日期:2017-12-25
通讯作者: Yinying KONG E-mail:kongcoco@hotmail.com
作者简介:Daochun SUN,1457330943@qq.com;Yingying HUO,fs_hyy@aliyun.com;Fujie CHAI,chaifujie@sina.com
基金资助:
The research was supported by the National Natural Science Foundation of China (11501127); Guangdong Natural Science Foundation (2015A030313628); the Training Plan for Outstanding Young Teachers in Higher Education of Guangdong (Yqgdufe1405) and the Open Fund of the National Higher Education Quality Monitoring Data Center (Guangzhou) (G1613).

THE INTEGRATION OF ALGEBROIDAL FUNCTIONS

Daochun SUN¹, Yingying HUO², Yinying KONG³, Fujie CHAI⁴

1. School of Mathematics, South China Normal University, Guangzhou 510631, China;
2. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China;
3. School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China;
4. Department of Mathematics, Guangzhou Civil Aviation College, Guangzhou 510403, China

Received:2016-02-29 Revised:2017-05-08 Online:2017-12-25 Published:2017-12-25
Contact: Yinying KONG E-mail:kongcoco@hotmail.com
Supported by:
The research was supported by the National Natural Science Foundation of China (11501127); Guangdong Natural Science Foundation (2015A030313628); the Training Plan for Outstanding Young Teachers in Higher Education of Guangdong (Yqgdufe1405) and the Open Fund of the National Higher Education Quality Monitoring Data Center (Guangzhou) (G1613).

摘要/Abstract

摘要：

In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the definition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros.

关键词: algebroidal function, integral, integral function element, direct continuation

Abstract:

Key words: algebroidal function, integral, integral function element, direct continuation

孙道椿, 霍颖莹, 孔荫莹, 柴富杰. THE INTEGRATION OF ALGEBROIDAL FUNCTIONS[J]. 数学物理学报(英文版), 2017, 37(6): 1861-1869.

Daochun SUN, Yingying HUO, Yinying KONG, Fujie CHAI. THE INTEGRATION OF ALGEBROIDAL FUNCTIONS[J]. Acta mathematica scientia,Series B, 2017, 37(6): 1861-1869.

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THE INTEGRATION OF ALGEBROIDAL FUNCTIONS

THE INTEGRATION OF ALGEBROIDAL FUNCTIONS

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