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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

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On the functional equation $f^{2}=e^{2\phi _{1}}+e^{2\phi _{2}}+e^{2\phi _{3}}\$ and a new Picard theorem
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by Mark Green PDF
Trans. Amer. Math. Soc. 195 (1974), 223-230 Request permission

Abstract:

By analogy with E. Borel’s reduction of the classical Picard theorem to an analytic statement about linear relations among exponentials of entire functions, a new Picard theorem is proved by considering the functional relation ${f^2} = {e^{2{\phi _1}}} + {e^{2{\phi _2}}} + {e^{2{\phi _3}}}$ for entire functions. The analytic techniques used are those of Nevanlinna theory.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 195 (1974), 223-230
  • MSC: Primary 30A70; Secondary 30A20
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0348112-4
  • MathSciNet review: 0348112