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Coefficient estimates concerning the Bieberbach conjecture. (English) Zbl 0285.30013

MSC:
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
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[1] Aharonov, D.: For the present the result is to be found in the Lecture Notes, University of Maryland (1972). A weaker result is proved in Proof of the Bieberbach conjecture for a certain class of univalent functions. Israel J. Math.8, 103-104 (1970) · Zbl 0203.38402 · doi:10.1007/BF02771305
[2] Ahlfors, L. V.: Conformal Invariants. New York: McGraw Hill, 1973 · Zbl 0272.30012
[3] Bazilevi?, J.: Zum Koeffizientenproblem der schlichten Funktionen. Mat. Sbornik, n. Ser.1, 210-228 (1936) · JFM 62.0372.01
[4] Bieberbach, L.: Über die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin, 940-955 (1916) · JFM 46.0552.01
[5] Bombieri, E.: On the local maximum property of the Koebe function. Inventiones math.4, 26-67 (1967) · Zbl 0174.12301 · doi:10.1007/BF01404579
[6] Ehrig, G.: The Bieberbach conjecture for univalent functions with restricted second coefficients. J. London math. Soc., II. Ser.8, 355-360 (1974) · Zbl 0286.30008 · doi:10.1112/jlms/s2-8.2.355
[7] Fekete, M., Szegö, G.: Eine Bemerkung über ungerade schlichte Funktionen. J. London math. Soc.8, 85-89 (1933) · Zbl 0006.35302 · doi:10.1112/jlms/s1-8.2.85
[8] FitzGerald, C. H.: Quadratic inequalities and coefficient estimates for schlicht functions. Arch. rat. Mech. Anal.46, 356-368 (1972) · Zbl 0242.30013 · doi:10.1007/BF00281102
[9] Gantmacher, F. R.: Matrizenrechnung I. Berlin: VEB Deutscher Verlag der Wissenschaften 1958
[10] Garabedian, P. R., Schiffer, M.: A proof of the Bieberbach conjecture for the fourth coefficient. J. rat. Mech. Anal.4, 427-465 (1955) · Zbl 0065.06902
[11] Garabedian, P. R., Ross, G. G., Schiffer, M.: On the Bieberbach conjecture for evenn. J. Math. Mech.14, 975-989 (1965) · Zbl 0141.26901
[12] Golusin, G. M.: On distortion theorems and the coefficients of univalent functions. Mat. Sbornik, n. Ser.19, 183-202 (1946) · Zbl 0063.01668
[13] Hayman, W. K.: The asymptotic behaviour ofp-valent functions. Proc. London math. Soc. III. Ser.5, 257-284 (1955) · Zbl 0067.30104 · doi:10.1112/plms/s3-5.3.257
[14] Jenkins, J. A.: Analytic Functions. Princeton: Princeton University Press 1960 · Zbl 0103.30002
[15] Löwner, K.: Untersuchungen über schlichte konforme Abbildungen des Einheitskreises I. Math. Ann.89, 103-121 (1923) · JFM 49.0714.01 · doi:10.1007/BF01448091
[16] Pederson, R. N.: A proof of the Bieberbach conjecture for the sixth coefficient. Arch. rat. Mech. Anal.31, 331-351 (1968) · Zbl 0184.10501 · doi:10.1007/BF00251415
[17] Pederson, R., Schiffer, M.: A proof of the Bieberbach conjecture for the fifth coefficient. Arch. rat. Mech. Anal.45, 161-193 (1972) · Zbl 0241.30025 · doi:10.1007/BF00281531
[18] Pommerenke, Ch.: Univalent Functions. Göttingen: Vandenhoeck & Ruprecht (To appear in 1974) · Zbl 0385.30013
[19] Schaeffer, A. C., Spencer, D. C.: Coefficient regions for schlicht functions. Amer. Math. Soc. Colloquium Publ. 35, New York 1950 · Zbl 0066.05701
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