On the maximum modulus points of entire and meromorphic functions

E. Ciechanowicz; I. Marchenko

We prove upper estimates for the number of separated maximum modulus points on the circle $|z|=r$ of both entire and meromorphic functions of finite lower order.

1. Baernstein A. Integral means, univalent functions and circular symmetrization, Acta Math. 133 (1974), no. 3–4, 139–169.

2. Essén M., Shea D. F. Applications of Denjoy integral inequalities and differential inequalities to growth problems for subharmonic and meromorphic functions, Proc. Roy. Irish Acad. A82 (1982), 201–216.

3. Gariepy R., Lewis J.L. Space analogues of some theorems for subharmonic and meromorphic functions, Ark. Mat. 13 (1975), 91–105.

4. Гольдберг А.А., Островский И.В. Распределение значений мероморфных функций, М.: Наука, 1970, 592 с.

5. Hayman W. K. Multivalent functions, Cambridge Univ. Press, Cambridge 1958.

6. Herzog F., Piranian G. The counting function for points of maximum modulus, Proceedings of Symposia in Pure Mathematics, 11 (1968), Entire functions and related parts analysis, Amer. Math. Soc., 240–243.

7. Marchenko I.I. On the magnitudes of deviations and spreads of meromorphic functions of finite lower order, Mat.Sb. 186 (1995), 391–408.

8. Неванлинна Р. Однозначные аналитические функции, М.: ОГИЗ, 1941, 388 c.

9. Петренко В.П. Рост мероморфных функций конечного нижнего порядка, Изв. Акад. Наук СССР 33 (1969), № 2, 414–454.

10. Ронкин Л.И. Введение в теорию целых функций многих переменных, М.: Наука, 1971, 430 с.

	On the maximum modulus points of entire and meromorphic functions
Author	E. Ciechanowicz, I. Marchenko ewa.ciechanowicz@wp.pl, marchenko@wmf.univ.szczecin.pl Institute of Mathematics, University of Szczecin ,Kharkiv State University ,
Abstract	We prove upper estimates for the number of separated maximum modulus points on the circle $\|z\|=r$ of both entire and meromorphic functions of finite lower order.
Keywords	upper estimate, separated maximum modulus point, finite lower order
DOI	doi:10.30970/ms.21.1.25-34
Reference	1. Baernstein A. Integral means, univalent functions and circular symmetrization, Acta Math. 133 (1974), no. 3–4, 139–169. 2. Essén M., Shea D. F. Applications of Denjoy integral inequalities and differential inequalities to growth problems for subharmonic and meromorphic functions, Proc. Roy. Irish Acad. A82 (1982), 201–216. 3. Gariepy R., Lewis J.L. Space analogues of some theorems for subharmonic and meromorphic functions, Ark. Mat. 13 (1975), 91–105. 4. Гольдберг А.А., Островский И.В. Распределение значений мероморфных функций, М.: Наука, 1970, 592 с. 5. Hayman W. K. Multivalent functions, Cambridge Univ. Press, Cambridge 1958. 6. Herzog F., Piranian G. The counting function for points of maximum modulus, Proceedings of Symposia in Pure Mathematics, 11 (1968), Entire functions and related parts analysis, Amer. Math. Soc., 240–243. 7. Marchenko I.I. On the magnitudes of deviations and spreads of meromorphic functions of finite lower order, Mat.Sb. 186 (1995), 391–408. 8. Неванлинна Р. Однозначные аналитические функции, М.: ОГИЗ, 1941, 388 c. 9. Петренко В.П. Рост мероморфных функций конечного нижнего порядка, Изв. Акад. Наук СССР 33 (1969), № 2, 414–454. 10. Ронкин Л.И. Введение в теорию целых функций многих переменных, М.: Наука, 1971, 430 с.
Pages	25-34
Volume	21
Issue	1
Year	2004
Journal	Matematychni Studii
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