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Common Borel directions of a meromorphic function with zero order and its derivative

Author(s): Tien-Yu Peter Chern
Journal: Proc. Amer. Math. Soc. 132 (2004), 1171-1175.
MSC (2000): Primary 30D30
Posted: October 2, 2003
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Abstract | References | Similar articles | Additional information

Abstract: There is a meromorphic function of zero order for which the function and its derivative have no common Borel direction.

References:

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H. H. Chen, Singular directions of meromorphic functions of order zero corresponding to Hayman's inequality (in Chinese), Acta Math. Sinica, 30 (1987), 234-237. MR 88h:30044

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Chia-tai Chuang, ``Un théorème relatif aux directions de Borel des fonctions méromorphes d'ordre fini, C. R. Acad. Sci. 204 (1937), 951-952.

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H. Milloux, Sur les directions de Borel des fonctions entières, de leurs dérivées et de leurs intégrales, J. Analyse Math., 1 (1951), 244-330. MR 13:930a

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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.

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M. Tsuji, Potential Theory in Modern Function Theory, Chelsea Publishing Co., New York, 1975. MR 54:2990

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G. Valiron,``Recherches sur le théorème de M. Borel dans la théorie des fonctions méromorphes", Acta Math. 52 (1928), 67-92.

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Guang-Hou Zhang, Common Borel directions of meromorphic functions and their successive derivatives or integrals I. (in Chinese), Acta Math. Sinica, no. 2, 20 (1977), 73-98. MR 80d:30022a

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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: pchern@math.msu.edu, tychern@isu.edu.tw

DOI: 10.1090/S0002-9939-03-07195-8
PII: S 0002-9939(03)07195-8
Keywords: Common Borel direction, zero order
Received by editor(s): May 17, 2002
Received by editor(s) in revised form: December 19, 2002
Posted: 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 of article: Copyright 2003, American Mathematical Society

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