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Transactions of the American Mathematical Society

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Non-Archimedean Nevanlinna theory
in several variables and
the non-Archimedean Nevanlinna inverse problem

Authors: William Cherry and Zhuan Ye
Journal: Trans. Amer. Math. Soc. 349 (1997), 5043-5071
MSC (1991): Primary 11J99, 11S80, 30D35, 32H30, 32P05
MathSciNet review: 1407485
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Abstract: Cartan's method is used to prove a several variable, non-Archimedean, Nevanlinna Second Main Theorem for hyperplanes in projective space. The corresponding defect relation is derived, but unlike in the complex case, we show that there can only be finitely many non-zero non-Archimedean defects. We then address the non-Archimedean Nevanlinna inverse problem, by showing that given a set of defects satisfying our conditions and a corresponding set of hyperplanes in projective space, there exists a non-Archimedean analytic function with the given defects at the specified hyperplanes, and with no other defects.

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Additional Information

William Cherry
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109

Zhuan Ye
Affiliation: Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115

Keywords: Non-Archimedean, Nevanlinna theory, $p$-adic, inverse problem, defect relations, projective space
Received by editor(s): October 14, 1995
Received by editor(s) in revised form: June 17, 1996
Additional Notes: Financial support for the first author was provided in part by NSF grant # DMS-9505041
Article copyright: © Copyright 1997 American Mathematical Society