Comptes Rendus
Analyse mathématique
Fonctions méromorphes aux zéros et pôles communs
[Meromorphic functions sharing the same zeros and poles]
Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 763-768.

Hinkkanen's problem (1984) is completely solved, i.e., it is shown that any meromorphic function f of one complex variable is determined by its zeros and poles and the zeros of f(j) for j=1,2,3,4.

On résout complètement le problème de Hinkkanen (1984) : les zéros et les pôles d'une fonction méromorphe quelconque f d'une variable complexe et les zéros de f(j), j=1,2,3,4, déterminent f.

Published online:
DOI: 10.1016/j.crma.2004.01.011

Günter Frank 1; Xinhou Hua 2; Rémi Vaillancourt 2

1 Technische Universität Berlin, Fachbereich 3 Mathematik, 10623 Berlin, Allemagne
2 Département de mathématiques et de statistique, Université d'Ottawa, Ottawa ON, K1N 6N5, Canada
     author = {G\"unter Frank and Xinhou Hua and R\'emi Vaillancourt},
     title = {Fonctions m\'eromorphes aux z\'eros et p\^oles communs},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {763--768},
     publisher = {Elsevier},
     volume = {338},
     number = {10},
     year = {2004},
     doi = {10.1016/j.crma.2004.01.011},
     language = {fr},
AU  - Günter Frank
AU  - Xinhou Hua
AU  - Rémi Vaillancourt
TI  - Fonctions méromorphes aux zéros et pôles communs
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 763
EP  - 768
VL  - 338
IS  - 10
PB  - Elsevier
DO  - 10.1016/j.crma.2004.01.011
LA  - fr
ID  - CRMATH_2004__338_10_763_0
ER  - 
%0 Journal Article
%A Günter Frank
%A Xinhou Hua
%A Rémi Vaillancourt
%T Fonctions méromorphes aux zéros et pôles communs
%J Comptes Rendus. Mathématique
%D 2004
%P 763-768
%V 338
%N 10
%I Elsevier
%R 10.1016/j.crma.2004.01.011
%G fr
%F CRMATH_2004__338_10_763_0
Günter Frank; Xinhou Hua; Rémi Vaillancourt. Fonctions méromorphes aux zéros et pôles communs. Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 763-768. doi : 10.1016/j.crma.2004.01.011.

[1] K.F. Barth; D.A. Brannan; W.K. Hayman Research problems in complex analysis, Bull. London Math. Soc., Volume 16 (1984), pp. 490-517

[2] C.T. Chuang Sur la comparaison de la croissance d'une fonction méromorphe et de celle de sa dérivée, Bull. Sci. Math., Volume 75 (1951), pp. 171-190

[3] J. Clunie On integral and meromorphic functions, J. London Math. Soc., Volume 37 (1962), pp. 17-27

[4] G. Frank; W. Hennekemper Einige Ergebnisse über die Werteverteilung meromorpher Funktionen und ihrer Ableitungen, Resultate Math., Volume 4 (1981), pp. 39-54

[5] F. Gross Factorization of Meromorphic Functions, U.S. Government Printing Office, Washington, DC, 1972

[6] G.G. Gundersen When two entire functions and also their first derivatives have the same zeros, Indiana Univ. Math. J., Volume 30 (1981), pp. 293-303

[7] G.G. Gundersen Meromorphic functions that share four values, Trans. Amer. Math. Soc., Volume 277 (1983), pp. 545-567 (Correction Trans. Amer. Math. Soc., 304, 1987, pp. 847-850)

[8] G. Frank, X.H. Hua, R. Vaillancourt, Meromorphic functions sharing the same zeros and poles, J. Can. Math./Can. J. Math., sous presse

[9] W.K. Hayman Meromorphic Functions, Oxford University Press, 1964

[10] X.H. Hua Some extensions of the Tumura–Clunie theorem, Complex Variables, Volume 16 (1991), pp. 69-77

[11] L. Köhler Meromorphic functions sharing zeros and poles and also some of their derivatives sharing zeros, Complex Variables, Volume 11 (1989), pp. 39-48

[12] I. Laine Nevanlinna Theory and Complex Differential Equations, de Gruyter, Berlin, 1993

[13] R. Nevanlinna Analytic Functions, Springer-Verlag, New York, 1970

[14] K. Tohge On a problem of Hinkkanen about Hadamard products, Kodai Math. J., Volume 13 (1990), pp. 101-120

[15] C.C. Yang On two entire functions which together with their first derivatives have the same zeros, J. Math. Anal. Appl., Volume 56 (1976), pp. 1-6

Cited by Sources:

Comments - Policy