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.
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.
Accepté le :
Publié le :
@article{CRMATH_2004__338_10_763_0,
author = {Frank, G\"unter and Hua, Xinhou and Vaillancourt, R\'emi},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.01.011/}
}
TY - JOUR AU - Frank, Günter AU - Hua, Xinhou AU - Vaillancourt, Rémi TI - Fonctions méromorphes aux zéros et pôles communs JO - Comptes Rendus. Mathématique PY - 2004 SP - 763 EP - 768 VL - 338 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.01.011/ DO - 10.1016/j.crma.2004.01.011 LA - fr ID - CRMATH_2004__338_10_763_0 ER -
%0 Journal Article %A Frank, Günter %A Hua, Xinhou %A Vaillancourt, Rémi %T Fonctions méromorphes aux zéros et pôles communs %J Comptes Rendus. Mathématique %D 2004 %P 763-768 %V 338 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.01.011/ %R 10.1016/j.crma.2004.01.011 %G fr %F CRMATH_2004__338_10_763_0
Frank, Günter; Hua, Xinhou; Vaillancourt, Rémi. Fonctions méromorphes aux zéros et pôles communs. Comptes Rendus. Mathématique, Tome 338 (2004) no. 10, pp. 763-768. doi : 10.1016/j.crma.2004.01.011. http://www.numdam.org/articles/10.1016/j.crma.2004.01.011/
[1] Research problems in complex analysis, Bull. London Math. Soc., Volume 16 (1984), pp. 490-517
[2] 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] On integral and meromorphic functions, J. London Math. Soc., Volume 37 (1962), pp. 17-27
[4] Einige Ergebnisse über die Werteverteilung meromorpher Funktionen und ihrer Ableitungen, Resultate Math., Volume 4 (1981), pp. 39-54
[5] Factorization of Meromorphic Functions, U.S. Government Printing Office, Washington, DC, 1972
[6] When two entire functions and also their first derivatives have the same zeros, Indiana Univ. Math. J., Volume 30 (1981), pp. 293-303
[7] 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] Meromorphic Functions, Oxford University Press, 1964
[10] Some extensions of the Tumura–Clunie theorem, Complex Variables, Volume 16 (1991), pp. 69-77
[11] Meromorphic functions sharing zeros and poles and also some of their derivatives sharing zeros, Complex Variables, Volume 11 (1989), pp. 39-48
[12] Nevanlinna Theory and Complex Differential Equations, de Gruyter, Berlin, 1993
[13] Analytic Functions, Springer-Verlag, New York, 1970
[14] On a problem of Hinkkanen about Hadamard products, Kodai Math. J., Volume 13 (1990), pp. 101-120
[15] On two entire functions which together with their first derivatives have the same zeros, J. Math. Anal. Appl., Volume 56 (1976), pp. 1-6
Cité par Sources :
