Papers of Alexandre Eremenko

The order is roughly chronological, all recent papers are available in ps and/or pdf. Only those links to journals are included which are free. If you want to see a paper whose ps/pdf file is not available, ask by e-mail, and I will send you a reprint or a photocopy.

  1. (with Ju. Gaida) Boundary operator in Boolean algebras with closure. English translation: Ukrainian Math. J., 26, 6 (1974) 662-664.
  2. (with V. S. Boichuk) The growth of entire functions represented by Dirichlet series, Izvestija vuzov, 5 (1975), 93-95 (Russian).
  3. Valiron deficiencies of entire characteristic functions. English translation: Ukrainian Math. J., 29, 6 (1978), 600-601.
  4. Growth of Nevanlinna proximity function. English translation: Siberian Math. J., 19, 3 (1979), 401-404.
  5. The set of asymptotic values of a meromorphic function of finite order. English translation: Math. Notes, 24, 5-6 (1979), 914-916.
  6. pdf (with A. Goldberg) Asymptotic curves of entire functions of finite order. English translation: Math. Sbornik, 37, 4 (1980), 509-513. (See also 47 and Rottenfusser-Ruckert-Rempe-Schleicher)
  7. An inequality for subharmonic functions. Function Theory, Functional Analysis and Applications, 29 (1978), 36-40.
  8. Letter to the editor. Function Theory, Functional Analysis and Applications, 32 (1979), 100 (Russian).
  9. Asymptotic curves of subharmonic functions in space. Izvestiya Acad. Nauk Armenian SSR, 14, 4 (1979) 292-296 (Russian).
  10. Growth of subharmonic functions on asymptotic curves. English translation: Soviet Math. Dokl., 20, 5 (1979), 943-945.
  11. On counting functions of sequences of a-points for functions holomorphic in the disk. Function Theory, Functional Analysis and Applications, 31 (1979), 59-62 (Russian).
  12. Growth of entire and subharmonic functions on asymptotic curves. English translation: Siberian Math. J., 21, 5 (1981), 573-683.
  13. (with N. Eremenko and M. Petrika) Correlation of myopia with muscular force of arms, J. of Ophthalmology, 6 (1981), 348-351 (Russian, English summary).
  14. An elementary remark on the set of entire solutions of a system of ordinary differential equations, ``Functional Analysis and Applied Mathematics'', Kiev, Naukova Dumka, 1982, 31-32 (Russian).
  15. Meromorphic solutions of algebraic differential equations, AMS Transl., v. 126 (1985), 1-3.
  16. (with A. Goldberg and I. Ostrovskii) On the sum of entire functions of completely regular growth, Dopovidi Ukrainian Acad. Sci., 2 (1982), 8-11 (Ukrainian, English summary).
  17. pdf Meromorphic solutions of algebraic differential equations. English translation: Russian Math. Surveys, 37, 4 (1982), 61-95. Correction: 38, 6 (1983). (See also 22 and 78).
  18. Meromorphic solutions of equations of Briot-Bouquet type. English translation: Amer. Math. Soc. Transl. (2) Vol. 133 (1986), 15-23. (See also Bergweiler-Rippon-Stallard and E-Liao-Ng (preprint)).
  19. (with A. Goldberg and I. Ostrovski) On the sum of entire functions of completely regular growth. Izvestiya Acad. Nauk Armenian SSR, 18, 1 (1983), 3-14 (Russian).
  20. Independence of some polynomial statistics from arithmetic mean. English translation: Ukrainian Math. J., 35, 3 (1983), 313-315.
  21. On deviations of meromorphic functions of finite lower order. Amer. Math. Soc. Transl., (2), 131 (1986), 45-54.
  22. On meromorphic solutions of algebraic differential equations of 1-st order. English translation: Functional Analysis and its Applications, 18, 3 (1984), 246-248.
  23. (with M. Lyubich) Iterates of entire functions. English translation: Soviet Math. Dokl., 30, 3 (1984), 592-594. (See also 57).
  24. (with A. Goldberg and M. Sodin) Defects and deviations of meromorphic functions of finite order. Dokl. Acad. Nauk Ukrainian SSR, N 10 (1984), 3-5 (Russian, Ukrainian).
  25. Defects and deviations of meromorphic functions of finite order. Dokl. Acad. Nauk Ukrainian SSR, N 1 (1985), 18-21 (Russian, Ukrainian).
  26. On the natural asymptotic curves of meromorphic functions. Complex Variables, 4 (1985), 305-309.
  27. (with M. Lyubich) Structural stability in some families on entire functions. English translation: Functional Analysis and its Applications, 19, 4 (1985), 323-324. (See also 57).
  28. Valiron exceptional values of entire functions of completely regular growth. Function Theory, Functional Analysis and Applications, 44 (1985), 48-52 (English translation: J. Soviet Math., 48, 3 (1989), 281).
  29. (with A. Goldberg) On the sets of range uniqueness for entire functions. Dokl. Acad. Sci. Armenian SSR, 81, 4 (1985), 159-161 (Russian).
  30. (with D. Shea and M. Sodin) On minimum modulus of entire function on Polya peaks. Function Theory, Functional Analysis and Applications, 45 (1986), 26-40 (English Transl.: J. Soviet Math., 48, 4 (1989), 386).
  31. The inverse problem of R. Nevanlinna theory, Doklady Armenian Acad. Sci., 82, 1 (1986), 2-5 (Russian, English summary).
  32. (with M. Sodin) A hypothesis of Littlewood and the distribution of values of entire functions. English translation: Functional Analysis and Appl., 20, N 1 (1986), 60-62. (See also Lewis and Wu, J. d'Analyse, 50 (1988)).
  33. Inverse problem of value distribution theory for meromorphic functions of finite order. English translation: Siberian Math. J., 27, 3 (1987), 377-390.
  34. pdf (with M. Sodin) Proof of a conditional theorem of Littlewood on the distribution of values of entire functions. English translation: Math USSR Izvestiya, 30, 2 (1988), 395-402. (See also Lewis and Wu, J. d'Analyse, 50 (1988)).
  35. On the set of deficient values of entire function of finite order. English translation: Ukrainian Math. J., 39, 3 (1987), 225-228.
  36. (with A. Goldberg and M. Sodin) Exceptional values in the sense of R. Nevanlinna and in the sense of V.P. Petrenko, I. Function Theory, Functional Analysis and Applications, (1987) 47, 41-50 (English translation: J. Soviet Math., 48, 6 (1989), 648.
  37. (with A. Goldberg and M. Sodin) Exceptional values in the sense of R. Nevanlinna and in the sense of V.P. Petrenko, II. Function Theory, Functional Analysis and Applications, (1987) 48, 48-70 (English translation: J. Soviet Math., 49, 2 (1990), 891.
  38. (with I.N. Baker) A problem on Julia sets. Ann. Acad. Sci. Fenn. Ser. A 1, Math., 12 (1987), 229-236. (See also Dinh and Levin-Przytycki, PAMS 125 (1997)).
  39. (with M. Lyubich) Examples of entire functions with pathological dynamics. J. London Math. Soc., (2) 36 (1987), 458-468.
  40. On entire functions bounded on the real axis. English translation: Soviet Math. Dokl., 37, 3 (1988), 693-695.
  41. New proof of Drasin's theorem on meromorphic functions of finite order with maximal deficiency sum I, Function Theory, Functional Analysis and their Application, (1989), 51, 107-116. English translation: Journal of Soviet Math., 52, 6 (1990), 3522-3529. (See also 64).
  42. New proof of Drasin's theorem on meromorphic functions of finite order with maximal deficiency sum II, Function Theory, Functional Analysis and their Application, 52 (1989) 69-77. English translation: Journal of Soviet Math 52, 5 (1990) 3397-3403. (See also 64).
  43. (with M. Lyubich) Dynamics of analytic transformations. Algebra and Analysis, 1, 3 (1989), 1-70 (Russian). Leningrad Math. J., 1, 3 (1990), 563-634 (English).
  44. Some functional equations connected with iteration of rational functions. Algebra and Analysis, 1, 4 (1989), 102-116 (Russian). Leningrad Math. J., 1, 4 (1990), 905-919 (English). (See also Dinh and Sibony).
  45. pdf (with G. Levin) On periodic points of polynomial. English translation: Ukrainian Mth. J., 41, 11 (1989), 1258-1262.
  46. On the iteration of entire functions. Dynamical Systems and Ergodic Theory. Banach Center Publications, 23, Warszawa, PWN, 1989, 339-345.
    (See also Rottenfusser-Ruckert-Rempe-Schleicher and Bergweiler)
  47. (with M. Sodin) On the behavior of an entire function on a sequence of concentric circles. Complex Variables, 12 (1989), 267-276.
  48. (with S. Ya. Khavinson, A. A. Kondratyuk, B. Ya. Levin, S. N. Mergelyan, I. V. Ostrovskii, M. N. Sheremeta, L. I. Volkovyskii) Anatolii Asirovich Goldberg (on his sixtieth birthday), Russian Math. Surveys, 45 (1990) 247-250.
  49. (with M. Sodin) The second main theorem of value distribution theory for meromorphic curves and non-linear divisors. Dokl. Acad. Nauk USSR (1990), 1293-1295 (English translation: Soviet Math. Dokl., 41, 2 (1990), 359-362.)
  50. (with M. Sodin) Iteration of rational functions and value distribution of Poincare functions. Function Theory, Functional Analysis and Applications, 53 (1990), 18-25 (English translation: J. Soviet Math., 58 (1992), 504-509.)
  51. (with M. Sodin) On meromorphic functions of finite order with maximal deficiency sum. Function Theory, Functional Analysis and Applications. 55, (1991) 84-95 (English translation: J. Soviet Math., 59 (1992), 643-651.)
  52. (with M. Sodin) Value distribution of meromorphic functions and meromorphic curves from the point of view of potential theory. Algebra \& analysis, 3, N 1 (1991), 131-164. (Russian). (English translation: St. Petersburg Math. J., 3 (1992), 109-136.)
  53. (with M. Sodin) On the distribution of values of meromorphic functions of finite order. Dokl. Acad. Nauk USSR 316, N 3 (1991), 538-541. (English translation: Soviet math. Dokl., 43 (1991), 128-131.)
  54. pdf Lower estimates in Littlewood's conjecture on mean spherical derivative of a polynomial. Proc. Amer. Math. Soc., 112, N 3 (1991), 713-715. (See also Lewis and Wu, J. d'Analyse, 50 (1988)).
  55. (with J. Lewis) Uniform limits of certain A-harmonic functions with applications to quasiregular mappings. Ann. Acad. Sci. Fenn., Ser. A. I., 1991, vol. 16, fasc. 2, 361-375. (See also Lewis, Proc. Amer. Math Soc., 122 (1994)).
  56. (with M. Ostrovskii and M. Sodin) On the support of the Riesz charge of a delta-subharmonic function, in: Operator Theory, subharmonic functions, Kiev, "Naukova Dumka", 1991, 50-54.
  57. pdf (with M. Lyubich) Dynamical properties of some classes of entire functions. Ann. Inst. Fourier, 42, 4 (1992), p. 1-32.
  58. (with B. Fuglede and M.Sodin) On the Riesz charge of the lower envelope of delta-subharmonic functions. Potential Analysis, 1992, vol. 1, N 2, 191-204.
  59. pdf A counterexample to the Arakelyan Conjecture. Bull. Amer. Math. Soc. 1992, vol. 27, N 1, p. 159-164. (See also Lewis and Wu, J. d'Analyse, 50 (1988)).
  60. (with T. Lyons) Finely open subsets in the limit set of a finitely generated Kleinian group. Published in the book: B. Fuglede et al. (ed.), Approximation by Solutions of Partial Differential Equations. NATO ASI Ser., C: Math. and Phys. Sci., vol. 365, Kluwer Acad. Publ., London, 1992; p. 61-67.
  61. (with M. Sodin) Parametrization of entire functions of sine-type by their critical values. In "Advances in Soviet mathematics", volume 11, 1992, AMS, 1992, p. 237-242. (See also G. Semmler).
  62. (with G. Levin) Estimates for characteristic exponents of a polynomial, Function Theory, Functional Analysis and Applications. 58, 1993, 30-39. (Russian, English transl.: J. Math. Sci. (New York) 85 (1997), no. 5, 2164--2171)
  63. (with J. Clunie and J. Rossi) On equilibrium points of logarithmic and Newtonian potential, Journal of the London Math. Soc., 47, 1993, 309-320.
  64. pdf and djvu Meromorphic functions with small ramification, Indiana University Math. Journal, 42, 4 (1993), 1193-1218.
  65. pdf On the characterization of a Riemann surface by its semigroup of endomorphisms. Trans. AMS 338, 1 (1993), 123-131.
  66. pdf (with G. Levin and M. Sodin) On the distribution of zeros of the Ruelle Zeta-Function, Comm. Math. Phys, 159, 3 (1994), 433-441.
  67. Two problems of potential theory arising in the study of the distribution of values of entire functions. ``Classical and Modern Potential Theory and Applications'', ed. K. Gowrisankaran et al., NATO ASI Ser., Math. Phys., vol. 430, Kluwer, London, 1994, p. 464-466.
  68. (with J. Langley and J. Rossi) On the zeros of meromorphic functions of the form $\sum_{k=1}^{\infty}\frac{a_k}{z-z_k}$. Journ. d'Analyse Math., 62 (1994), 271-286.
  69. pdf (with L. Lempert) An extremal problem for polynomials, Proc. AMS., 122, 1 (1994), 191-193. (See also 116).
  70. ps pdf (with W. Bergweiler) On the singularities of the inverse to a meromorphic function of finite order, Revista math. iberoamericana, 11 (1995), 355-373.
  71. pdf (with D. Hamilton) On the area distortion by quasiconformal mappings, Proc. AMS, 123, 9 (1995), 2793-2797.
  72. pdf (with L. Rubel) On the zero sets of certain entire functions, Proc. AMS., 124, 8 (1996), 2401-2404.
  73. pdf A counterexample to Cartan's conjecture on holomorphic curves omitting hyperplanes, Proc. AMS, 124, 10 (1996), 3097-3100. (See also 75).
  74. pdf (with L. Rubel) The arithmetic of entire functions under composition, Adv. Math., 124, 2 (1996), 334-354.
  75. ps pdf Holomorphic curves omitting five planes in projective space, American J. Math., 118, 6 (1996), 1141-1151.
  76. Entire and meromorphic solutions of ordinary differential equations, Chapter 6 in the book: Complex Analysis I, Encyclopaedia of Mathematical Sciences, vol. 85; Springer, NY, 1997, 141-153.
  77. An analogue of the defect relation for the uniform metric, Complex Variables, Theory and Appl., 34 (1997), 83-97.
  78. ps pdf Rational solutions of first-order differential equations, Ann. Acad. Sci. Fenn., Math., v. 23, 1998, 181-190. Corrected version.
  79. ps pdf Extremal holomorphic curves for defect relations, J. d'Analyse math., vol. 74, 1998, 307-323.
  80. An analogue of the defect relation for the uniform metric, II, Complex Variables, Theory and Appl., 37, 1998, 145-159.
  81. ps pdf (with I. Ostrovskii and M. Sodin) Anatolii Asirovich Gol'dberg, Complex variables, Theory and Appl., 37, 1998, 1-51.
  82. ps pdf A Picard type theorem for holomorphic curves, Periodica Mathematica Hungarica, 38, 1-2 (1999), 39-42. (See also 119).
  83. ps pdf (with W. Hayman) On the length of lemniscates, Michigan Math. J., 46 (1999), 409-415. Corrected version.
  84. ps pdf (with M. Bonk) Schlicht regions for entire and meromorphic functions, J. d'Analyse 77, 1999, 69-104. (See also 93).
  85. ps pdf (with W. Hayman) Univalent functions of fast growth with gap power series, Math. Proc. Cambridge Phil. Soc., 127 (1999), 525-532.
  86. pdf (with A. Atzmon and M. Sodin) Spectral inclusion and analytic continuation, Bull. London Math. Soc., 31 (1999), 722-728.
  87. ps pdf (with M. Bonk) Surfaces singulières de fonctions méromorphes, CRAS, 329, (1999), 953-955. (See also 93).
  88. ps pdf Bloch radius, normal families and quasiregular mappings, Proc. Amer. Math. Soc., 128 (2000), 557-560. (See also K. Rajala, Proc. AMS, 132 (2004)).
  89. ps pdf Ahlfors' contribution to the theory of meromorphic functions, in the book: R. Brooks and M. Sodin, eds., Lectures in Memory of Lars Ahlfors, Israel Math. Conf. Proc., vol. 14, AMS, Providence RI, 2000, pp. 41-63.
  90. ps pdf (with M. Bonk) Uniformly hyperbolic surfaces, Indiana Univ. Math. J. 49, 1 (2000), 61-80.
  91. ps pdf (with W. Bergweiler) Entire function of slow growth whose Julia set coincides with the plane, Ergod. Theory and Dyn. Syst. 20 (2000), 1-6. Correction: 21 (2001), 637. Corrected version.
  92. ps pdf (with W. Hayman) On a conjecture of Danikas and Ruscheweyh, in: P. Ricci, ed., Problemi attuali dell'analisi e della fisica matematica, dedicato alla memoria del Prof. Gaetano Fichera, Aracne, Roma, 2000, p. 17-24.
  93. ps pdf (with M. Bonk) Covering properties of meromorphic functions, negative curvature and spherical geometry, Ann of Math. 152 (2000), 551-592.
  94. ps pdf (with A. Gabrielov) Wronski map and Grassmannians of real codimension 2 subspaces, Computational Methods and Function Theory, 1 (2001) 1-25.
  95. ps pdf (with A. Gabrielov) Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry, Ann of Math., 155 (2002), 105-129. (See also Eremenko, Gabrielov and Mukhin, Tarasov, Varchenko)
  96. ps pdf (with A. Gabrielov) Counterexamples to pole placement by static output feedback, Linear Algebra and Appl., 351-352 (2002) 211-218. (See also 99).
  97. ps pdf (with A. Gabrielov) Degrees of real Wronski maps, Discrete and Computational Geometry, 28 (2002) 331--347.
  98. ps pdf Value distribution and potential theory, Proceedings of the International Congress of Mathematicians, vol. 2, p. 681-690, Higher Education Press, Beijing, 2002.
  99. ps pdf (with A. Gabrielov) Pole placement by static output feedback for generic linear systems, SIAM J. on Control and Opt., 41, 1 (2002) 303--312.
  100. (with W. Hayman) On the length of lemniscates, in the book: Paul Erdos and his Mathematics. I, Bolyai Society, Budapest, 2002 241--242.
  101. ps pdf (with W. Bergweiler and J. Langley) Real entire functions of infinite order and a conjecture of Wiman, GAFA, 13, 5 (2003), 975-991.
  102. ps pdf (with D. Novikov) Oscillation of functions with a spectral gap, Proc. Nat. Acad. Sci., 101, 16 (2004), 5872-5873.
  103. ps pdf (with D. Novikov) Oscillation of Fourier integrals with a spectral gap, J. de Math. Pures et Appl., 8, 3 (2004), 313-365.
  104. ps pdf Geometric theory of meromorphic functions, in the book: In the Tradition of Ahlfors-Bers, III, (Contemp. math., 355) AMS, Providence, RI, 2004, pp. 221-230. (Here is an Expanded version).
  105. ps pdf Transcendental meromorphic functions with three singular values, Illinois J. Math., 48 (2004), 701-709.
  106. ps pdf Metrics of positive curvature with conic singularities on the sphere, Proc. AMS, 132 (2004), 11, 3349--3355.
  107. ps pdf Critical values of generating functions of totally positive sequences, Matematicheskaya fizika, analiz, geometriya, 11 (2004), 4, 1-13. (Math. Physics, Analysis and Geometry (MAG)).
  108. ps pdf html (with A. Baernstein II, A. Fryntov and A. Solynin) Sharp estimates for hyperbolic metrics and covering theorems of Landau type, Ann. Acad. Sci. Fenn. Math. 30 (2005) 113-133.
  109. ps pdf (with W. Bergweiler and J. Langley) Zeros of differential polynomials in real meromorphic functions, Proc. Edinburgh Math. Soc. (2005) 48 1-15.
  110. ps pdf (with S. Merenkov) Nevanlinna functions with real zeros, Illinois J. Math., 49, 3-4 (2005) 1093--1110.
  111. ps pdf (with A. Gabrielov, M. Shapiro and A. Vainshtein) Rational functions and real Schubert calculus, Proc. AMS, 134 (2006), no. 4, 949--957.
  112. ps pdf Meromorphic traveling wave solutions of the Kuramoto-Sivashinsky equation, J. Math. Phys., Anal. Geom. (Kharkov), 2 (2006) N 3 278-286.
  113. ps pdf A Toda lattice in dimension 2 and Nevanlinna theory, J. Math. Phys., Anal. Geom. (Kharkov), 31 (2007) 39-46.
  114. ps pdf Exceptional values in holomorphic families of entire functions, Michigan Math. J., 54, 3 (2006) 687-696.
  115. ps pdf (with W. Bergweiler) Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions, Acta math., 197, 2 (2006), 125-146.
  116. ps pdf A Markov-type inequality for arbitrary plane continua, Proc. AMS, 135 (2007) 1505-1510.
  117. ps pdf (with Peter Yuditskii) Uniform approximation of sgn(x) by polynomials and entire functions, J. d'Analyse Math., 101 (2007) 313-324.
  118. ps pdf (with A. Gabrielov and B. Shapiro) High energy eigenfunctions of one-dimensional Schrodinger operators with polynomial coefficients, Computational Methods and Function Theory, 8 (2008). No. 2, 513--529.
  119. pdf ps (with N. Nadirashvili and D. Jakobson) On nodal sets and nodal domains in the sphere and in the plane, Ann. Inst. Fourier, 57 (2007) 2345-2360.
  120. ps pdf (with W. Bergweiler) Meromorphic functions with two completely invariant domains,
    in the book: Ph. Rippon and G. Stallard, eds, Transcendental Dynamics and Complex Analysis, p. 74-89 (LMS Lect. Notes Ser., 348) Cambridge UP, 2008
  121. ps pdf (with I. Ostrovskii) On the ``pits effect'' of Littlewood and Offord,
    Bull. London Math. Soc., 39 (2007) 929-939.
  122. ps pdf (with A. Gabrielov and B. Shapiro) Zeros of eigenfunctions of some anharmonic oscillators, Ann. Inst. Fourier, Grenoble, 58, 2 (2008) 603-624.

    Accepted

  123. ps pdf (with W. Cherry) Landau's theorem for holomorphic curves in projective space and the Kobayashi metric on hyperplane complement,
    Pure and Appl. Math. Quarterly.
  124. ps pdf (with J. Langley) A survey of some results after 1970 (Appendix to the English translation of A. Goldberg and I. Ostrovskii, Distribution of values of meromorphic functions, Moscow 1970, to appear in AMS).
  125. ps pdf (with W. Bergweiler) Direct singularities and completely invariant domains of entire functions,
    Illinois J. Math.
  126. ps pdf (with L. W. Liao and T. W. Ng) Meromorphic solutions of higher order Briot-Bouquet differential equations,
    Math. Proc. Cambridge Philos. Soc.

    Preprints