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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Developments in the classical Nevanlinna theory of meromorphic functions

Author(s): W. H. J. Fuchs
Journal: Bull. Amer. Math. Soc. 73 (1967), 275-291.
MathSciNet review: 0207989
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References | Additional information

References:

A. W. K. Hayman, Meromorphic functions, Oxford Univ. Press, New York, 1964 MR 164038

B. K. L. Hiong, Sur les fonctions méromorphes et fonctions algébroides, Mémor. Sci. Math. no. 139, Gauthier-Villars, Paris, 1957. MR 91341

C. R. Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars, Paris, 1929.

D. R. Nevanlinna, Eindeutige analytische Funktionen, 2nd ed., Springer, Berlin, 1953. MR 57330

E. H. Wittich, Neuere Untersuchungen über eindeutige analytische Funktionen, Springer, Berlin, 1955. MR 77620

F. L. Sario and K. Noshiro, Value distribution theory, Van Nostrand, Princeton, N. J., 1966. MR 215998

G. H. Weyl and J. Weyl, Meromorphic functions and analytic curves, Princeton Univ. Press, Princeton, N. J., 1943. MR 9057

1.
L. V. Ahlfors, The theory of meromorphic curves, Acta Soc. Sci. Fenn. A(2) 3, No. 4 (1941), 31 pp. MR 4309
2.
J. M. Anderson, Asymptotic properties of integral functions of genus zero, Quart. J. Math. Oxford Ser. (2) 16 (1965), 151-164. MR 179357
3.
J. M. Anderson, Growth properties of integral and sub-harmonic functions, J. Analyse Math. 13 (1964), 355-389. MR 180686
4.
N. U. Arakelyan, Entire functions of finite order with infinitely many deficient values, International Congress of Mathematicians, Moscow, 1966.
5.
K. Arima, On maximum modulus of integral functions, J. Math. Soc. Japan 4 (1952), 62-66. MR 49320
6.
R. Bott and S. S. Chern, Hermitian vector bundles and the equidistribution of the zeros of their holomorphic sections, Acta Math. 114 (1965), 71-112. MR 185607
7.
S. S. Chern, Complex analytic mappings of Riemann surfaces. I, Amer. J. Math. 82 (1960), 323-337. MR 115183
8.
A. Edrei, Meromorphic functions with three radially distributed values, Trans. Amer. Math. Soc. 78 (1955), 276-293. MR 67982
9.
A. Edrei, Meromorphic functions with values that are both deficient and asymptotic, Studies in Mathematical Analysis and Related Topics, Stanford Univ. Press, Stanford, Calif., 1962. MR 153843
10.
A. Edrei, The deficiencies of functions of finite lower order, Duke Math. J. 31 (1964), 1-22. MR 158079
11.
A. Edrei, Sums of deficiencies of meromorphic functions, J. Analyse Math. 14 (1965), 79-107. MR 180678
12.
A. Edrei, Sums of deficiencies of meromorphic functions. II, J. Analyse Math. (to appear). MR 215996
13.
A. Edrei and W. H. J. Fuchs, On the growth of meromorphic functions with several deficient values, Trans. Amer. Math. Soc. 93 (1959), 292-328. MR 109887
14.
A. Edrei, Valeurs déficientes et valeurs asymptotiques des fonctions méromorphes, Comment. Math. Helv. 33 (1959), 258-295. MR 123716
15.
A. Edrei, On the deficiencies of meromorphic functions of order less than one, Duke Math. J. 27 (1960), 233-250. MR 123717
16.
A. Edrei, Bounds for the number of deficient values of certain classes of meromorphic functions, Proc. London Math. Soc. 12 (1962), 317-344. MR 138765
17.
A. Edrei, On meromorphic functions with regions free of poles and zeros, Acta Math. 108 (1962), 113-145. MR 142759
18.
A. Edrei, W. H. J. Fuchs, and S. Hellerstein, Radial distribution and the deficiencies of the values of a meromorphic function, Pacific J. Math. 11 (1961), 135-151. MR 122999
19.
M. Essén, A theorem on the maximum modulus of entire functions, Math. Scand. 17 (1965), 161-168. MR 197727
20.
W. H. J. Fuchs, A theorem on the Nevanlinna deficiencies of meromorphic functions of finite order, Ann. of Math. 68 (1958), 203-209. MR 100677
21.
W. H. J. Fuchs, Proof of a conjecture of G. Polya concerning gap series, Illinois J. Math. 7 (1963), 661-667. MR 159933
22.
W. H. J. Fuchs and W. K. Hayman, An entire function with assigned deficiencies, Studies in Mathematical Analysis and Related Topics, Stanford Univ. Press, Stanford, Calif., 1962, pp. 117-125. MR 153844
23.
A. A. Goldberg, On the inverse problem of the theory of distribution of values of meromorphic functions, Ukrain. Math. J. 6 (1954), 385-397. (Ukrainian) MR 69886
24.
A. A. Goldberg, On the defects of meromorphic functions, Dokl. Akad. Nauk SSSR 98 (1954), 893-895. (Russian) MR 71543
25.
A. A. Goldberg, On a problem in the theory of the distribution of values of meromorphic functions, Dopovidi Akad. Nauk Ukraïn. RSR (1954), No. 1. (Ukrainian) MR 69885
26.
A. A. Goldberg, Some asymptotic properties of meromorphic functions, Učen. Zap. Lvov. Univ. 38 (1956), 54-73. (Russian)
27.
A. A. Goldberg, Example of an entire function of finite order with a non-asymptotic deficient value, Učen. Zap. Užgorod. Univ. 18 (1957), 191-194. (Russian)
28.
A. A. Goldberg, On meromorphic functions with separated zeros and poles, Izv. Vysš. Učebn. Zaved. Matematika (1960) No. 4 (17), 67-72. (Russian) MR 131551
29.
A. A. Goldberg, Distribution of values of meromorphic functions with separated zeros and poles, Dokl. Akad. Nauk SSSR 137 (1961), 1030-1033=Soviet Math. Dokl. 2 (1961), 389-392. MR 118832
30.
A. A. Goldberg, Remark on the theorem of Tumura-Clunie, Dokl. Užgorod Univ., Phys.-Mat. series 1961 (No. 4), 109-110. (Russian)
31.
A. A. Goldberg, On a theorem of M. G. Krein, Dokl. Užgorod Univ., Phys.-Mat. series (1961), 106-108. (Russian)
32.
A. A. Goldberg, On the growth of entire functions along a ray, Dokl. Akad. Nauk SSSR 152 (1963), 1049-1050=Soviet Math. Dokl. 4 (1963), 1491-1493. MR 154990
33.
A. A. Goldberg, Three examples of entire functions, Dopovidi Akad. Nauk Ukraïn. RSR (1963), 443-445. (Ukrainian) MR 165106
34.
A. A. Goldberg, On the lower order of an entire function with a finite deficient value, Sibirsk. Mat. Ž. 5 (1964), 54-76. (Russian) MR 160905
35.
A. A. Goldberg, On the size of the lower order of an entire function with a deficient value, Dokl. Akad. Nauk SSSR 159 (1964), 968-970=Soviet Math. Dokl. 5 (1964), 1631-1633. MR 170006
36.
A. A. Goldberg and I. V. Ostrovskii, New investigations on the growth and the distribution of values of entire and meromorphic functions of zero, Uspehi Mat. Nauk 16 (1961), 51-62. (Russian) MR 132187
37.
A. A. Goldberg and I. V. Ostrovskii, Some theorems on the growth of meromorphic functions, Učen. Zap. Kharkov Univ., Series 5 (1961), 3-37. (Russian)
38.
A. A. Goldberg and V. G. Tairova, On entire functions with two finite totally ramified values, Zap. Mech. Mat., Faculty of Kharkov University 29, Ser. 4 (1963), 67-78.
39.
W. K. Hayman, An integral function with a defective value that is neither asymptotic nor invariant under change of origin, J. London Math. Soc. 28 (1953), 369-376. MR 54705
40.
W. K. Hayman, On the characteristic of functions meromorphic in the unit disk and of their integrals, Acta Math. 112 (1964), 181-214. MR 168763
41.
W. K. Hayman, On the characteristic of functions meromorphic in the plane and of their integrals, Proc. London Math. Soc. (3) 14a (1965), 93-128. MR 180679
42.
S. Hellerstein, On a class of meromorphic functions with deficient zeros and poles, Pacific J. Math. 13 (1963), 115-124. MR 152655
43.
B. Kjellberg, On the minimum modulus of entire functions of lower order less than one, Math. Scand. 8 (1960), 189-197. MR 125967
44.
B. Kjellberg, On the minimum modulus of entire functions, Math. Scand. 12 (1963), 5-11. MR 159942
45.
T. Kövari, A gap theorem for entire functions of infinite order, Michigan Math. J. 12 (1965), 133-140. MR 176076
46.
B. Ja. Levin and I. V. Ostrovskii, On the dependence of the rate of growth of an entire function on the distribution of the zeros of its derivative (on a quéstion of G. Polya and A. Wiman), Sibirsk. Mat. Ž. 1 (1960), 427-455. (Russian) MR 130979
47.
I. V. Ostrovskii, On meromorphic functions assuming some values at points close to a finite set of rays, Dokl. Akad. Nauk SSSR 120 (1958), 970-972. (Russian) MR 101323
48.
I. V. Ostrovskii, On the distribution of zeros of the derivative of an entire function all of whose zeros are close to the real axis, Dokl. Akad. Nauk SSSR 130 (1960), 973-976=Soviet Math. Dokl. 1 (1960), 114-117. MR 139739
49.
I. V. Ostrovskii, On the relation between the growth of a meromorphic function and the angular distribution of its values, Dokl. Akad. Nauk SSSR 132 (1960), 48-52=Soviet Math. Dokl. 1 (1960), 485-488. MR 124497
50.
I. V. Ostrovskii, Bounds on the deficiencies of meromorphic functions two of whose values are only taken on in an angle, Izv. Vysš. Učebn. Zaved. Matematika (1960), 138-148. (Russian) MR 130980
51.
I. V. Ostrovskii, On the relation between the growth of a meromorphic function and the angular distribution of its values, Izv. Akad. Nauk SSSR 25 (1961), 277-328. (Russian) MR 124498
52.
I. V. Ostrovskii, On the deficiencies of meromorphic functions of lower order less than one, Dokl. Akad. Nauk SSSR 150 (1963), 32-35=Soviet Math. Dokl. 4 (1963), 587-591. MR 148921
53.
I. V. Ostrovskii, On a problem of the distribution of values, Dokl. Akad. Nauk SSSR 151 (1963), 34-37.=Soviet Math. Dokl. 4 (1963), 909-913. MR 152656
54.
R. E. A. C. Paley, A note on integral functions, Proc. Cambridge Philos. Soc. 28 (1932), 262-265.
55.
V. P. Petrenko, Some estimates of the logarithmic derivative of a meromorphic function, Izv. Akad. Nauk Armjan. SSR 17 (1964), 24-37. (Russian) MR 165108
56.
V. P. Petrenko, On the size of the deficiencies of meromorphic functions, Dokl. Akad. Nauk SSSR 158 (1964), 1030-1033=Soviet Math. Dokl. 5 (1964), 1357-1361. MR 167625
57.
V. P. Petrenko, The growth of a meromorphic function on a ray, Dokl. Akad. Nauk SSSR 155 (1964), 281-284=Soviet Math. Dokl. 5 (1964), 405-408. MR 160911
58.
A. Pfluger, Zur Defektrelation ganzer Funktionen endlicher Ordnung, Comment. Math. Helv. 19 (1946), 91-104. MR 17806
59.
A. Pfluger and G. Pólya, On the power series of an integral function having an exceptional value, Proc. Cambridge Philos. Soc. 31 (1935), 153-155.
60.
L. Sario, Value distribution under analytic mappings of arbitrary Riemann surfaces, Acta Math. 109 (1963), 1-10. MR 145066
61.
L. Sario, General value distribution theory, Nagoya Math. J. 23 (1963), 213-229. MR 168754
62.
Mme. L. Schwartz, Exemple d'une fonction méromorphe ayant des valeurs déficientes non asymptotiques, C. R. Acad. Sci. Paris 212 (1941), 382-384. MR 4308
63.
H. Selberg, Über die Wertverteilung der algebroiden Funktionen, Math. Z. 31 (1930), 709-728. MR 1545143
64.
H. Selberg, Algebroide Funktionen und Umkehrfunktionen Abelscher Integrale, Avh. Norske Vid.-Akad. Oslo, Mat./Naturv. Kl. no. 8 (1934).
65.
D. F. Shea, On the Valiron deficiencies of meromorphic functions of finite order, Trans. Amer. Math. Soc. 124 (1966), 201-227. MR 200458
66.
O. Teichmüller, Vermutungen und Sätze über die Wertverteilung bei gebrochenen Funktionen, Deutsche Math. 4 (1939), 163-190.
67.
G. Valiron, Sur le minimum du module des fonctions entières d'ordre inférieur à un, Mathematica 11 (1935), 264-269.


Additional Information:

DOI: 10.1090/S0002-9904-1967-11718-X
PII: S 0002-9904(1967)11718-X




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