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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 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Further results on fixpoints and zeros of entire functions
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by Jian Hua Zheng and Chung-Chun Yang
Trans. Amer. Math. Soc. 347 (1995), 37-50
DOI: https://doi.org/10.1090/S0002-9947-1995-1179403-9

Abstract:

In this paper, a quantitative estimation on the number of zeros of the function $f \circ g(z) - \alpha (z)$ is derived, where $f$ and $g$ are transcendental entire functions and $\alpha (z)$ a nonconstant polynomial. As an application of this and a further step towards an affirmative answer to a conjecture of Baker, a quantitative estimation on the number of period points of exact order $n$ of ${f_n}$ ($n$th iterate of $f$) is obtained.
References
  • Irvine Noel Baker, Zusammensetzungen ganzer Funktionen, Math. Z. 69 (1958), 121–163 (German). MR 97532, DOI 10.1007/BF01187396
  • I. N. Baker, Fixpoints and iterates of entire functions, Math. Z. 71 (1959), 146–153. MR 107015, DOI 10.1007/BF01181396
  • I. N. Baker, Some entire functions with fixpoints of every order, J. Austral. Math. Soc. 1 (1959/1961), 203–209. MR 0114007, DOI 10.1017/S1446788700025556
  • Walter Bergweiler, Proof of a conjecture of Gross concerning fix-points, Math. Z. 204 (1990), no. 3, 381–390. MR 1107470, DOI 10.1007/BF02570881
  • Walter Bergweiler, On the fix-points of composite functions, Pacific J. Math. 143 (1990), no. 1, 1–8. MR 1047396, DOI 10.2140/pjm.1990.143.1
  • —, Periodic points of entire functions: Proof of a conjecture of Baker (to appear).
  • J. Clunie, The composition of entire and meromorphic functions, Mathematical Essays Dedicated to A. J. Macintyre, Ohio Univ. Press, Athens, Ohio, 1970, pp. 75–92. MR 0271352
  • F. Gross and C. F. Osgood, On fixed points of composite entire functions, J. London Math. Soc. (2) 28 (1983), no. 1, 57–61. MR 703464, DOI 10.1112/jlms/s2-28.1.57
  • W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. MR 0164038
  • W. K. Hayman, On the characteristic of functions meromorphic in the plane and of their integrals, Proc. London Math. Soc. (3) 14a (1965), 93–128. MR 180679, DOI 10.1112/plms/s3-14A.1.93
  • W. K. Hayman, Research problems in function theory, The Athlone Press [University of London], London, 1967. MR 0217268
  • W. K. Hayman, Value distribution and A.P. gaps, J. London Math. Soc. (2) 28 (1983), no. 2, 327–338. MR 713387, DOI 10.1112/jlms/s2-28.2.327
  • R. Nevanlinna, Le théorème de Picard-Borel et la théorème des fonctions meromorphes, Gauthier-Villars, Paris, 1929. G. S. Prokopovich, Fixpoints of meromorphic functions, Ukrain. Mat. Zh. 25 (1973), 248-260; English transl., Ukrainian Math. J. pp. 198-208. P. C. Rosenbloom, The fixpoints of entire functions, Medd. Lunds Univ. Mat. Sem. [Tome Suppl.] (1952), 187-192. G. Valiron, Lectures on the general theory of integral functions, Edonard Privat, Toulouse, 1923.
  • Le Yang, Zhi fenbu lun ji qi xin yanjiu, Chuncui Shuxue yu Yingyong Shuxue Zhuanzhu [Series of Monographs in Pure and Applied Mathematics], vol. 9, Kexue Chubanshe (Science Press), Beijing, 1982 (Chinese). MR 724784
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Bibliographic Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 37-50
  • MSC: Primary 30D05; Secondary 30D20
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1179403-9
  • MathSciNet review: 1179403