On algebroid solutions of algebraic differential equations in the complex plane, II

Nobushige TODA

doi:10.2969/jmsj/04540705

Nobushige TODA

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JOURNAL FREE ACCESS

1993 Volume 45 Issue 4 Pages 705-717

DOI https://doi.org/10.2969/jmsj/04540705

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Published: 1993 Received: July 02, 1992 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Kikuji Matsumoto on the occasion of his sixtieth birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S. B. Bank and R. P. Kaufman, On the growth of meromorphic solutions of the differential equation (y')ⁿ=R(z, y), Acta Math., 144 (1980), 223-248.
2) A. E. Eremenko, Meromorphic solutions of algebraic differential equations, Russian Math. Surveys, 37 (1982), 61-95.
3) F. Gackstatter and I. Laine, Zur Theorie der gewöhnlichen Differentialgleichungen im Komplexen, Ann. Polon. Math., 38 (1980), 259-287.
4) W. K. Hayman, Meromorphic functions, Oxford Univ. Press, 1964.
5) W. K. Hayman and F. M. Stewart, Real inequalities with application to function theory, Proc. Cambridge Philos. Soc., 50 (1954), 250-260.
6) He Yuzan and I. Laine, The Hayman-Miles theorem and the differential equation (y')ⁿ=R(z, y), Analysis, 10 (1990), 387-396.
7) I. Laine, On the behaviour of the solutions of some first order differential equations, Ann. Acad. Sci. Fenn. Ser. A Math., 497 (1971).
8) A. Z. Mokhon'ko, Estimates of Nevanlinna characteristics of algebroid functions and their applications to differential equations, Siberian Math. J., 23 (1982), 80-88.
9) J. von Rieth, Untersuchngen gewisser Klassen gewöhnlicher Differentialgleichungen erster und zweiter Ordnung im Komplexen, Doctoral Dissertation, Technische Hochschule, Aachen, 1986.
10) H. Selberg, Über die Wertverteilung der algebroiden Funktionen, Math. Z., 31 (1930), 709-728.
11) T. Takagi, Lecture on Algebra, Kyoritsu, Tokyo, 1957 (in Japanese).
12) N. Toda, On algebroid solutions of binomial differential equations in the complex plane, Proc. Japan Acad., 64A (1988), 61-64.
13) N. Toda, On algebroid solutions of some algebraic differential equations in the complex plane, Proc. Japan Acad., 65A (1989), 94-97.
14) N. Toda, On algebroid solutions of algebraic differential equations in the complex plane, Rev. Roumaine Math. Pures Appl., 36 (1991), 457-464.
15) E. Ullrich, Über den Einfluss der Verzweigtheit einer Algebroide auf ihre Wert- verteilung, J. Reine Angew. Math., 167 (1931), 198-220.
16) G. Valiron, Sur la dérivée des fonctions algébroïdes, Bull. Soc. Math. France, 59 (1931), 17-39.
17) K. Yosida, A generalization of Malmquist's theorem, Japan. J. Math., 9 (1933), 253-256.
18) K. Yosida, On algebroid solutions of ordinary differential equations, Japan. J. Math., 10 (1933), 199-208.

Right : [1] S. B. Bank and R. P. Kaufman, On the growth of meromorphic solutions of the differential equation (y')ⁿ=R(z, y), Acta Math., 144 (1980), 223-248.
[2] A. E. Eremenko, Meromorphic solutions of algebraic differential equations, Russian Math. Surveys, 37 (1982), 61-95.
[3] F. Gackstatter and I. Laine, Zur Theorie der gewöhnlichen Differentialgleichungen im Komplexen, Ann. Polon. Math., 38 (1980), 259-287.
[4] W. K. Hayman, Meromorphic functions, Oxford Univ. Press, 1964.
[5] W. K. Hayman and F. M. Stewart, Real inequalities with application to function theory, Proc. Cambridge Philos. Soc., 50 (1954), 250-260.
[6] He Yuzan and I. Laine, The Hayman-Miles theorem and the differential equation (y')ⁿ=R(z, y), Analysis, 10 (1990), 387-396.
[7] I. Laine, On the behaviour of the solutions of some first order differential equations, Ann. Acad. Sci. Fenn. Ser. A Math., 497 (1971).
[8] A. Z. Mokhon'ko, Estimates of Nevanlinna characteristics of algebroid functions and their applications to differential equations, Siberian Math. J., 23 (1982), 80-88.
[9] J. von Rieth, Untersuchngen gewisser Klassen gewöhnlicher Differentialgleichungen erster und zweiter Ordnung im Komplexen, Doctoral Dissertation, Technische Hochschule, Aachen, 1986.
[10] H. Selberg, Über die Wertverteilung der algebroiden Funktionen, Math. Z., 31 (1930), 709-728.
[11] T. Takagi, Lecture on Algebra, Kyoritsu, Tokyo, 1957 (in Japanese).
[12] N. Toda, On algebroid solutions of binomial differential equations in the complex plane, Proc. Japan Acad., 64A (1988), 61-64.
[13] N. Toda, On algebroid solutions of some algebraic differential equations in the complex plane, Proc. Japan Acad., 65A (1989), 94-97.
[14] N. Toda, On algebroid solutions of algebraic differential equations in the complex plane, Rev. Roumaine Math. Pures Appl., 36 (1991), 457-464.
[15] E. Ullrich, Über den Einfluss der Verzweigtheit einer Algebroide auf ihre Wertverteilung, J. Reine Angew. Math., 167 (1931), 198-220.
[16] G. Valiron, Sur la dérivée des fonctions algébroïdes, Bull. Soc. Math. France, 59 (1931), 17-39.
[17] K. Yosida, A generalization of Malmquist's theorem, Japan. J. Math., 9 (1933), 253-256.
[18] K. Yosida, On algebroid solutions of ordinary differential equations, Japan. J. Math., 10 (1933), 199-208.

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