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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Common Borel directions of a meromorphic function with zero order and its derivative
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by Tien-Yu Peter Chern PDF
Proc. Amer. Math. Soc. 132 (2004), 1171-1175 Request permission


There is a meromorphic function of zero order for which the function and its derivative have no common Borel direction.
  • Huai Hui Chen, Singular directions of meromorphic functions of order zero corresponding to Hayman’s inequality, Acta Math. Sinica 30 (1987), no. 2, 234–237 (Chinese). MR 891931
  • Chia-tai Chuang, “Un théorème relatif aux directions de Borel des fonctions méromorphes d’ordre fini, C. R. Acad. Sci. 204 (1937), 951-952.
  • C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
  • A. Rauch, Cas ou une direction de Borel d’une fonction entière $f(z)$ d’ordre finite est aussi direction de Borel pour $f’(z)$, C. R. Acad. Sci., 199 (1934), 1014-1016.
  • John Rossi, A sharp result concerning cercles de remplissage, Ann. Acad. Sci. Fenn. Ser. A I Math. 20 (1995), no. 1, 179–185. MR 1304116
  • M. Tsuji, Potential theory in modern function theory, Chelsea Publishing Co., New York, 1975. Reprinting of the 1959 original. MR 0414898
  • G. Valiron,“Recherches sur le théorème de M. Borel dans la théorie des fonctions méromorphes", Acta Math. 52 (1928), 67-92.
  • Lo Yang, Value distribution theory, Springer-Verlag, Berlin; Science Press Beijing, Beijing, 1993. Translated and revised from the 1982 Chinese original. MR 1301781
  • Guang Hou Zhang, Common Borel directions of meromorphic functions and their successive derivatives or integrals. I, Acta Math. Sinica 20 (1977), no. 2, 73–98 (Chinese). MR 513593
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Additional Information
  • Tien-Yu Peter Chern
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • Address at time of publication: Department of Applied Mathematics, I-Shou University, Kaohsiung 840, Taiwan
  • Email:,
  • Received by editor(s): May 17, 2002
  • Received by editor(s) in revised form: December 19, 2002
  • Published electronically: October 2, 2003
  • Additional Notes: This paper was supported in part by the NSC R.O.C. under the contract NSC 92-2115-M-214-004, a fund from Academia Sinica (Taipei, Taiwan), and a fund from Michigan State University, U.S.A
  • Communicated by: Juha M. Heinonen
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1171-1175
  • MSC (2000): Primary 30D30
  • DOI:
  • MathSciNet review: 2045434