The error term in Nevanlinna theory. II
Author:
Serge Lang
Journal:
Bull. Amer. Math. Soc. 22 (1990), 115-125
MSC (1985):
Primary 11J68, 30D35, 32H30
DOI:
https://doi.org/10.1090/S0273-0979-1990-15857-4
MathSciNet review:
1003864
Full-text PDF Free Access
References | Similar Articles | Additional Information
- William W. Adams, Asymptotic Diophantine approximations to $e$, Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 28–31. MR 186626, DOI https://doi.org/10.1073/pnas.55.1.28
- William W. Adams, Asymptotic diophantine approximations and Hurwitz numbers, Amer. J. Math. 89 (1967), 1083–1108. MR 222030, DOI https://doi.org/10.2307/2373420
- W. Adams and S. Lang, Some computations in diophantine approximations, J. Reine Angew. Math. 220 (1965), 163–173. MR 182608, DOI https://doi.org/10.1515/crll.1965.220.163
- Lars V. Ahlfors, The theory of meromorphic curves, Acta Soc. Sci. Fennicae. Nova Ser. A 3 (1941), no. 4, 31. MR 4309
- A. D. Brjuno, The expansion of algebraic numbers into continued fractions, Ž. Vyčisl. Mat i Mat. Fiz. 4 (1964), 211–221 (Russian). MR 163884
- James Carlson and Phillip Griffiths, A defect relation for equidimensional holomorphic mappings between algebraic varieties, Ann. of Math. (2) 95 (1972), 557–584. MR 311935, DOI https://doi.org/10.2307/1970871
- Shiing-shen Chern, Complex analytic mappings of Riemann surfaces. I, Amer. J. Math. 82 (1960), 323–337. MR 115183, DOI https://doi.org/10.2307/2372738
- Phillip A. Griffiths, Entire holomorphic mappings in one and several complex variables, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1976. The fifth set of Hermann Weyl Lectures, given at the Institute for Advanced Study, Princeton, N. J., October and November 1974; Annals of Mathematics Studies, No. 85. MR 0447638
- Phillip Griffiths and James King, Nevanlinna theory and holomorphic mappings between algebraic varieties, Acta Math. 130 (1973), 145–220. MR 427690, DOI https://doi.org/10.1007/BF02392265
- Serge Lang, Report on diophantine approximations, Bull. Soc. Math. France 93 (1965), 177–192. MR 193064
- Serge Lang, Asymptotic Diophantine approximations, Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 31–34. MR 188155, DOI https://doi.org/10.1073/pnas.55.1.31
- Serge Lang, Introduction to diophantine approximations, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0209227
- Serge Lang, Transcendental numbers and diophantine approximations, Bull. Amer. Math. Soc. 77 (1971), 635–677. MR 289424, DOI https://doi.org/10.1090/S0002-9904-1971-12761-1
- Serge Lang, The error term in Nevanlinna theory, Duke Math. J. 56 (1988), no. 1, 193–218. MR 932862, DOI https://doi.org/10.1215/S0012-7094-88-05609-8
- Serge Lang and Hale Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972). MR 306131, DOI https://doi.org/10.1007/978-1-4612-2120-3_5
- S. Lang and H. Trotter, Addendum to: “Continued fractions for some algebraic numbers” (J. Reine Angew. Math. 255 (1972), 112–134), J. Reine Angew. Math. 267 (1974), 219–220. MR 349593
- Rolf Nevanlinna, Analytic functions, Die Grundlehren der mathematischen Wissenschaften, Band 162, Springer-Verlag, New York-Berlin, 1970. Translated from the second German edition by Phillip Emig. MR 0279280
- John von Neumann and Bryant Tuckerman, Continued fraction expansion of $2^{1/3}$, Math. Tables Aids Comput. 9 (1955), 23–24. MR 68900, DOI https://doi.org/10.1090/S0025-5718-1955-0068900-3
- Charles F. Osgood, A number theoretic-differential equations approach to generalizing Nevanlinna theory, Indian J. Math. 23 (1981), no. 1-3, 1–15. MR 722894
- Charles F. Osgood, Sometimes effective Thue-Siegel-Roth-Schmidt-Nevanlinna bounds, or better, J. Number Theory 21 (1985), no. 3, 347–389. MR 814011, DOI https://doi.org/10.1016/0022-314X%2885%2990061-7
- R. D. Richtmyer, Marjorie Devaney, and N. Metropolis, Continued fraction expansions of algebraic numbers, Numer. Math. 4 (1962), 68–84. MR 136574, DOI https://doi.org/10.1007/BF01386297
- K. F. Roth, Rational approximations to algebraic numbers, Mathematika 2 (1955), 1–20; corrigendum, 168. MR 72182, DOI https://doi.org/10.1112/S0025579300000644
- Wolfgang M. Schmidt, Diophantine approximation, Lecture Notes in Mathematics, vol. 785, Springer, Berlin, 1980. MR 568710
- Paul Vojta, Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, vol. 1239, Springer-Verlag, Berlin, 1987. MR 883451
- Paul Vojta, A refinement of Schmidt’s subspace theorem, Amer. J. Math. 111 (1989), no. 3, 489–518. MR 1002010, DOI https://doi.org/10.2307/2374670
- Pit-Mann Wong, On the second main theorem of Nevanlinna theory, Amer. J. Math. 111 (1989), no. 4, 549–583. MR 1011549, DOI https://doi.org/10.2307/2374813
Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 11J68, 30D35, 32H30
Retrieve articles in all journals with MSC (1985): 11J68, 30D35, 32H30