On the length of lemniscates

Michigan Mathematical Journal

Volumn 46, Issue 2, 1999, Pages 409-415

  Eremenko, Alexandre ^a   Hayman, Walter ^b  

^a PURDUE UNIVERSITY   (United States)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038851335     PISSN: 00262285     EISSN: None     Source Type: Journal    
DOI: 10.1307/mmj/1030132418     Document Type: Article

References (12)

1. L. Ahlfors, Lectures on quasiconformal mappings, Van Nostrand, New York, 1966.
2. P. Borwein, The arc length of the lemniscate {|p(z)| = 1}, Proc. Amer. Math. Soc. 123 (1995), 797-799.
3. L. Carleson and T. Gamelin, Complex dynamics, Springer-Verlag, New York, 1993.
4. P. Erdos, F. Herzog, and G. Piranian, Metric properties of polynomials, J. Analyse Math. 6 (1958), 125-148.
5. W. Hayman, Research problems in function theory, Athlone Press, London, 1967.
6. E. Hille, Analytic functions theory, vol. II, Ginn & Co., Boston, 1962.
7. B. Ya. Levin, Distribution of zeros of entire functions, Transl. Math. Monographs, 5, Amer. Math. Soc., Providence, RI, 1980.
8. Ch. Pommerenke, Über die Kapazität ebener Kontinuen, Math. Ann. 139 (1959), 64-75.
9. _, Einige Sätze über die Kapazität ebener Mengen, Math. Ann. 141 (1960), 143-152.
10. _, On metric properties of complex polynomials, Michigan Math. J. 8 (1961), 97-115.
11. V. V. Prasolov and Yu. P. Soloviev, Elliptic functions and elliptic integrals, Transl. Math. Monographs, 170, Amer. Math. Soc., Providence, RI, 1997.
12. L. Santalo, Integral geometry and geometric probability, Addison-Wesley, Reading, MA, 1976.