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The value-distribution of lacunary series and a conjecture of Paley. (English) Zbl 0437.30021

##### MSC:
 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30B10 Power series (including lacunary series) in one complex variable
##### Keywords:
Hadamard lacunary series; Peano curve
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##### References:
 [1] J.M. ANDERSON, Boundary properties of analytic functions with gap power series, Quart. J. Math. Oxford, (2) 21 (1970), 247-256. · Zbl 0209.37801 [2] K.G. BINMORE, R. HORNBLOWER, Boundary behaviour of functions with Hadamard gaps, Nagoya Math. J., 48 (1972), 173-181. · Zbl 0244.30029 [3] I.L. CHANG, On the zeros of power series with Hadamard gaps-distribution in sectors, Trans. of the Amer. Math. Soc., 178 (1973), 393-400. · Zbl 0229.30009 [4] W.H.J. FUCHS, On the zeros of power series with Hadamard gaps, Nagoya Math. J., 29 (1967), 167-174. · Zbl 0172.36902 [5] W.H.J. FUCHS, Topics in Nevanlinna theory, Proc. NRL Conference on classical function theory, Math. Rec. Center, Naval Research Laboratory, Washington, D.C., 1970, 1-32. · Zbl 0294.30021 [6] J.P. KAHANE, Lacunary Taylor and Fourier series, Bull. Amer. Math. Soc., 70 (1964), 199-213. · Zbl 0121.30102 [7] J.P. KAHANE, G. WEISS, M. WEISS, On lacunary power series, Arkiv för Math., B.5 No 1 (1963), 1-26. · Zbl 0134.05701 [8] T. MURAI, Sur la distribution des valeurs des séries lacunaires, J. of the London Math. Soc. (2), 21 (1980), 93-110. · Zbl 0449.30017 [9] T. MURAI, Une conjecture de Paley sur séries de Taylor lacunaires, C.R.A.S., Paris, t. 290 (2 juin 1980), 947-948. · Zbl 0443.30001 [10] R.E.A.C. PALEY, On lacunary power series, Proc. Nat. Acad. Sci. U.S.A., 19 (1933), 271-272. · JFM 59.0320.03 [11] R. SALEM, A. ZYGMUND, Lacunary power series and Peano curves, Duke J. of Math., 12 (1945), 569-578. · Zbl 0060.20402 [12] M. WEISS, Concerning a theorem of Paley on lacunary trigonometric series, Acta Math., 102 (1959), 225-238. · Zbl 0091.06702 [13] G. WEISS, M. WEISS, On the Picard property of lacunary power series, Studia Math., 22 (1963), 221-245. · Zbl 0111.27202 [14] A. ZYGMUND, Trigonometric series I, II, Cambridge, 1959. · Zbl 0085.05601
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