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A Second Main Theorem on ℙn for difference operator

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Abstract

The main result of this article is an extension of the Second Main Theorem, of Halburd and Korhonen, for meromorphic functions of finite order. Their result replaces the counting function of the ramification divisor N ramf(r) in the classical Second Main Theorem by the counting function of a finite difference divisor N pair(r). In this article, the Second Main Theorem of Halburd and Korhonen is extended to the case of holomorphic maps into ℙn of finite order.

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Authors and Affiliations

  1. Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Pit-Mann Wong

  2. Department of Mathematics, University of Hong Kong, Hong Kong, China

    Hiu-Fai Law & Philip P. W. Wong

Authors
  1. Pit-Mann Wong
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  2. Hiu-Fai Law
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  3. Philip P. W. Wong
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Corresponding author

Correspondence to Pit-Mann Wong.

Additional information

Dedicated to Professor ZHONG TongDe on the occasion of his 80th birthday

This work was supported by Natural Science Foundation of USA (Grant No. DMS0713348) and Research Grant Council of Hong Kong (Grant No. HKU7053/06P)

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Wong, PM., Law, HF. & Wong, P.P.W. A Second Main Theorem on ℙn for difference operator. Sci. China Ser. A-Math. 52, 2751–2758 (2009). https://doi.org/10.1007/s11425-009-0213-5

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  • DOI: https://doi.org/10.1007/s11425-009-0213-5

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