no. 1
The value-distribution of lacunary series and a conjecture of Paley
Annales de l'Institut Fourier, Volume 31 (1981) no. 1, pp. 135-156.

The purpose of this paper is to establish a theorem which answers a conjecture of Paley on the distribution of values of Hadamard lacunary series and which is useful to study the Peano curve property of such series.

Le but de cet article est d’établir un théorème qui répond à une conjecture de Paley sur la distribution des valeurs des séries lacunaires à la Hadamard et qui est utile pour étudier la propriété de courbe de Peano de telles séries.

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     title = {The value-distribution of lacunary series and a conjecture of {Paley}},
     journal = {Annales de l'Institut Fourier},
     pages = {135--156},
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Murai, Takafumi. The value-distribution of lacunary series and a conjecture of Paley. Annales de l'Institut Fourier, Volume 31 (1981) no. 1, pp. 135-156. doi : 10.5802/aif.820. http://www.numdam.org/articles/10.5802/aif.820/

[1] J.M. Anderson, Boundary properties of analytic functions with gap power series, Quart. J. Math. Oxford, (2) 21 (1970), 247-256. | Zbl

[2] K.G. Binmore, R. Hornblower, Boundary behaviour of functions with Hadamard gaps, Nagoya Math. J., 48 (1972), 173-181. | MR | Zbl

[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. | MR | Zbl

[4] W.H.J. Fuchs, On the zeros of power series with Hadamard gaps, Nagoya Math. J., 29 (1967), 167-174. | MR | Zbl

[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. | MR | Zbl

[6] J.P. Kahane, Lacunary Taylor and Fourier series, Bull. Amer. Math. Soc., 70 (1964), 199-213. | MR | Zbl

[7] J.P. Kahane, G. Weiss, M. Weiss, On lacunary power series, Arkiv för Math., B.5 No 1 (1963), 1-26. | MR | Zbl

[8] T. Murai, Sur la distribution des valeurs des séries lacunaires, J. of the London Math. Soc. (2), 21 (1980), 93-110. | MR | Zbl

[9] T. Murai, Une conjecture de Paley sur séries de Taylor lacunaires, C.R.A.S., Paris, t. 290 (2 juin 1980), 947-948. | MR | Zbl

[10] R.E.A.C. Paley, On lacunary power series, Proc. Nat. Acad. Sci. U.S.A., 19 (1933), 271-272. | JFM | Zbl

[11] R. Salem, A. Zygmund, Lacunary power series and Peano curves, Duke J. of Math., 12 (1945), 569-578. | MR | Zbl

[12] M. Weiss, Concerning a theorem of Paley on lacunary trigonometric series, Acta Math., 102 (1959), 225-238. | MR | Zbl

[13] G. Weiss, M. Weiss, On the Picard property of lacunary power series, Studia Math., 22 (1963), 221-245. | MR | Zbl

[14] A. Zygmund, Trigonometric series I, II, Cambridge, 1959. | Zbl

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