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

Cherry, William; Ye, Zhuan

doi:10.1090/S0002-9947-97-01874-6

Non-Archimedean Nevanlinna theory in several variables and the non-Archimedean Nevanlinna inverse problem
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by William Cherry and Zhuan Ye PDF

Trans. Amer. Math. Soc. 349 (1997), 5043-5071 Request permission

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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