An Ahlfors Islands Theorem for non-archimedean meromorphic functions
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- by Robert L. Benedetto PDF
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Abstract:
We present a $p$-adic and non-archimedean version of Ahlfors’ Five Islands Theorem for meromorphic functions, extending an earlier theorem of the author for holomorphic functions. In the non-archimedean setting, the theorem requires only four islands, with explicit constants. We present examples to show that the constants are sharp and that other hypotheses of the theorem cannot be removed.References
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Additional Information
- Robert L. Benedetto
- Affiliation: Department of Mathematics and Computer Science, Amherst College, Amherst,Massachusetts 01002
- MR Author ID: 647128
- Email: rlb@cs.amherst.edu
- Received by editor(s): May 16, 2006
- Published electronically: March 11, 2008
- Additional Notes: The author gratefully acknowledges the support of a Miner D. Crary Research Fellowship from Amherst College
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 4099-4124
- MSC (2000): Primary 30G06; Secondary 11J97, 12J25
- DOI: https://doi.org/10.1090/S0002-9947-08-04546-7
- MathSciNet review: 2395165