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Nevanlinna theory via
holomorphic forms
Xianjing Dong and Shuangshuang Yang |
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Vol. 319 (2022), No. 1, 55–74
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Abstract |
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This paper redevelops Nevanlinna theory for meromorphic functions on in the viewpoint of holomorphic forms. According to our observation, Nevanlinna’s functions can be formulated by a holomorphic form. Applying this thought to Riemann surfaces, one then extends the definition of Nevanlinna’s functions using a holomorphic form . With the new settings, an analogue of Nevanlinna theory for the -exhausted Riemann surfaces is obtained, which is viewed as a generalization of the classical Nevanlinna theory for and . |
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Keywords
Nevanlinna theory, value distribution, second main theorem,
defect relation, Riemann surface
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Mathematical Subject Classification
Primary: 30D35
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Milestones
Received: 4 January 2022
Revised: 26 April 2022
Accepted: 27 May 2022
Published: 28 August 2022
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Authors |
| Xianjing Dong | |
| School of Mathematical
Sciences Qufu Normal University Qufu China |
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| Shuangshuang Yang | |
| Department of Mathematics Nanjing University Nanjing China |
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