Vol. 319, No. 1, 2022

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Nevanlinna theory via holomorphic forms

Xianjing Dong and Shuangshuang Yang

Vol. 319 (2022), No. 1, 55–74

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 𝒮. With the new settings, an analogue of Nevanlinna theory for the 𝒮-exhausted Riemann surfaces is obtained, which is viewed as a generalization of the classical Nevanlinna theory for and 𝔻.

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Nevanlinna theory, value distribution, second main theorem, defect relation, Riemann surface
Mathematical Subject Classification
Primary: 30D35
Received: 4 January 2022
Revised: 26 April 2022
Accepted: 27 May 2022
Published: 28 August 2022
Xianjing Dong
School of Mathematical Sciences
Qufu Normal University
Shuangshuang Yang
Department of Mathematics
Nanjing University