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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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


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
  • MR Author ID: 292846
  • Email:
  • Zhuan Ye
  • Affiliation: Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115
  • Email:
  • 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
  • © Copyright 1997 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 349 (1997), 5043-5071
  • MSC (1991): Primary 11J99, 11S80, 30D35, 32H30, 32P05
  • DOI:
  • MathSciNet review: 1407485