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Murai, Takafumi

The deficiency of entire functions with Fejer gaps. (English) Zbl 0489.30028

Ann. Inst. Fourier 33, No. 3, 39-58 (1983).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0489.30028

Cited in 11 Documents

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30D10 Representations of entire functions of one complex variable by series and integrals

Keywords:

deficiency; Fejer gap; Fabry gap
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References:

[1] [1] , Sur les équations algébriques contenant des paramètres arbitraires, Bull. Int. Acad. Polon. Sci. Lett., Sér. A (III) (1927), 542-685. · JFM 56.0863.02
[2] [2] , Sur les fonctions entières à séries lacunaires, C.R.A.S., Paris, Sér. A-B, 187 (1928), 477-479. · JFM 54.0349.02
[3] [3] , On integral functions with exceptional values, J. London Math. Soc., 42 (1967), 393-400. · Zbl 0164.08701
[4] [4] , Über die Wurzel vom kleinsten absoluten Betrage einer algebraischen Gleichung, Math. Annalen, (1908), 413-423. · JFM 39.0123.02
[5] [5] , Proof of a conjecture of G. Pólya concerning gap series, Illinois J. Math., 7 (1963), 661-667. · Zbl 0113.28702
[6] [6] , Nevanlinna theory and gap series, Symposia on theoretical physics and mathematics, V.9, Plenum Press, New York, 1969. · Zbl 0179.11001
[7] [7] , Meromorphic functions, Oxford, 1964. · Zbl 0115.06203
[8] [8] , Angular value distribution of power series with gaps, Proc. London Math. Soc., (3), 24 (1972), 590-624. · Zbl 0239.30035
[9] [9] , On the Borel exceptional values of lacunary integral functions, J. Analyse Math., 9 (1961/1962), 71-109. · Zbl 0101.05302
[10] [10] , A gap-theorem for entire functions of infinite order, Michigan Math. J., 12 (1965), 133-140. · Zbl 0152.06604
[11] [11] , The deficiency of gap series, Analysis (1983) to appear. · Zbl 0533.30028
[12] [12] , Growth of meromorphic functions of finite lower order, Izv. Akad. Nauk SSSR, Ser. Mat., 33 (1969), 414-454. · Zbl 0194.11101
[13] [13] , Lücken und Singularitäten von Porenzreihen, Math. Z., 29 (1929), 549-640. · JFM 55.0186.02
[14] [14] , An analogue of a theorem of W.H.J. Fuchs on gap series, Proc. London Math. Soc., (3), 21 (1970), 525-539. · Zbl 0206.08801
[15] [15] , Über den Zusammenhang zwischen dem Maximalbetrage einer analytischen Function und dem grössten Gliede der zugehörigen Taylorschen Reihe, Acta Math., 37 (1914), 305-326. · JFM 45.0641.02
[16] [16] , Trigonometric series I, Cambridge, 1959. · Zbl 0085.05601
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