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Advances in complex function theory: Proceedings of seminars by W. E. Kirwan, L. Zalcman

By W. E. Kirwan, L. Zalcman

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5 (1955), 257-284. 5. K. Hayman, Multivalent 1958. 6. J. Korevaar, Another numerical Tauberian theorem for power series, Nederl. Akad. Wetensch. Proc. Set. A. 57 -Indagationes Math. 16 (1954), 4 6 - 5 6 . 7. E. Landau, Darstellung und BeKr~ndung einiKer neuerer ErKebnisse der Funktionentheorie, Zweite Auflage, J. Springer, Berlin, 1929. 8. M. Milin, Haymants regularity theorem for the coefficients of univalent functions, Dokl. Akad. Nauk. SSSR 192 (1970), 738-741 (in Russian). 9. M. Milin, Univalent Functions and Orthonormal "Nauka", Moscow, 1971 (in Russian).

7 (1959), 53-77. 9. A. Huber, Uber Wachstuniseigenschaften gewissen Klassen yon subharmonischen Funktionen, Comment. Math. Helv. 26 (1952), 81-116. Meromorphic Functions, Oxford, 1964. i0. U. Kuran, On the zeros of harmonic functions, Soc. 44 ( 1 9 6 9 ) , 303-309. ii. U. Kuran, Generalizations of a theorem on harmonic functions, J. London Math. Soc. 41 (1966)~ 145-152. 12. G. P61ya and g. SzegS, Isoperimetric Inequalities i__nn Mathematical Physics, Princeton Univ. Press, 1951. 13. E. Schmidt, Die Brunn-Minkowskische Ungleichung und ihr Sp~egelbild sowie die isoperimetrische Eigenschaft der Kugel in der euklidischen und nichteuklidischen geometric, I.

Lo__ Llog of o r d e r k < 2 TM. that let l 2J n first " with at least k tracts, as r e q u i r e d . that 1 p = [ n, is e v e n Now a function ~ n, Next in find 2xm-i ( ii m-I 1 - 4x 2} the c o r o l l a r y . -_ T h e n we bound > 2 m. We s u p p o s e we h a v e q = I. Thus ~1 (n+l) 2 integer, first 1 p : ~ (n+l), that m = 3. q : 0, while Then if n we h a v e k : ~1 we d e f i n e n to be the or {(n+l)2_l} smallest integer that (n+l) T h e n we can find (n+l) 2 = 2k I a function 2 > 2k.

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