THE INTEGRATION OF ALGEBROIDAL FUNCTIONS

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

Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (6): 1861-1869.doi: 10.1016/S0252-9602(17)30112-1

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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).

Abstract

Abstract:

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.

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

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

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