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An analogue of continued fractions in number theory for Nevanlinna theory


Author: Zhuan Ye
Journal: Trans. Amer. Math. Soc. 356 (2004), 4829-4838
MSC (2000): Primary 30D35, 11J70
DOI: https://doi.org/10.1090/S0002-9947-04-03709-2
Published electronically: June 25, 2004
MathSciNet review: 2084400
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Abstract | References | Similar Articles | Additional Information

Abstract: We show an analogue of continued fractions in approximation to irrational numbers by rationals for Nevanlinna theory. The analogue is a sequence of points in the complex plane which approaches a given finite set of points and at a given rate in the sense of Nevanlinna theory.


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  • 1. H. Chen and Z. Ye, The error term in Nevanlinna's inequality, Science in China (Series A), 43, (2000), 1060-1066. MR 1802149 (2001k:30039)
  • 2. W. Cherry and Z. Ye, Nevanlinna's Theory of Value Distribution, Springer-Verlag, Monographs in Math., 2001. MR 1831783 (2002h:30030)
  • 3. W. Hayman, Meromorphic Functions, Clarendon Press, 1964. MR 0164038 (29:1337)
  • 4. A. Hinkkanen, A sharp form of Nevanlinna's second fundamental theorem, Invent. Math., 108, (1992), 549-574. MR 1163238 (93c:30045)
  • 5. A. Ya. Khinchin, Continued Fractions, Chicago University Press, 1964. MR 0161833 (28:5037)
  • 6. S. Lang, The error term in Nevanlinna theory, Duke Math. J., 56, (1988), 193-218. MR 0932862 (89g:32037)
  • 7. S. Lang, The error term in Nevanlinna theory, Bull. of the AMS, 22, (1990), 115-125. MR 1003864 (90k:32080)
  • 8. S. Lang, Introduction to Diophantine Approximations, Springer-Verlag, 1995. MR 1348400 (96h:11067)
  • 9. S. Lang and W. Cherry, Topics in Nevanlinna Theory, Springer-Verlag, Lecture Notes in Math., 1433, 1990. MR 1069755 (91k:32025)
  • 10. S. Lang and H. Trotter, Continued fractions of some algebraic numbers, J. reine u. angew. Math., 255, (1972), 112-134. MR 0306131 (46:5258)
  • 11. J. Miles, A sharp form of the lemma on the logarithmic derivative, J. London Math. Soc., 45, (1992), 243-254. MR 1171552 (93i:30026)
  • 12. R. Nevanlinna, Analytic Functions, Springer, 1970. MR 0279280 (43:5003)
  • 13. C. F. Osgood, Sometimes effective Thue-Siegel-Roth-Schimidt Nevanlinna bounds or better, J. Number Theory, 21, (1985), 347-398. MR 0814011 (87f:11046)
  • 14. M. Ru, Nevanlinna Theory and its Relation to Diophantine Approximation, World Scientific Publishing Co. Inc., 2001. MR 1850002 (2002g:11106)
  • 15. M. Ru and P. Vojta, Schmidt's subspace theorem with moving targets, Invent. Math., 127, (1997), 51-65. MR 1423025 (97g:11076)
  • 16. L. R. Sons and Z. Ye, The best error terms of classical functions, Complex Variables, 28, (1995), 55-66. MR 1700264 (2000f:30020)
  • 17. P. Vojta, Diophantine Approximations and Value Distribution Theory, Springer-Verlag, Lecture Notes in Math., 1239, 1987. MR 0883451 (91k:11049)
  • 18. P. Vojta, Nevanlinna theory and Diophantine approximation, Math. Sci. Res. Inst. Publ., 37, (1999), 535-564. MR 1748613 (2001j:11072)
  • 19. Y. Wang, Sharp forms of Nevanlinna's error terms, J. Anal. Math., 71, (1997), 87-102. MR 1454245 (98f:30033)
  • 20. P. M. Wong and W. Stoll, Second main theorem of Nevanlinna theory for non-equidimensional meromorphic maps, Amer. J. Math., 116, (1994), 1031-1071. MR 1296724 (95g:32042)
  • 21. Z. Ye, On Nevanlinna's error terms, Duke Math. J., 64, (1991), 243-260. MR 1136375 (93a:30039)
  • 22. Z. Ye, On Nevanlinna's second main theorem in projective space, Invent. Math., 122, (1995), 475-507. MR 1359601 (96j:32030)
  • 23. Z. Ye, An analogue of Khinchin's theorem in Diophantine approximation for Nevanlinna theory, XVII Rolf Nevanlinna Colloquium; Walter de Gruyter and Company, (1996), 309-319. MR 1427096 (97h:30046)

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Additional Information

Zhuan Ye
Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115
Email: ye@math.niu.edu

DOI: https://doi.org/10.1090/S0002-9947-04-03709-2
Keywords: Continued fraction, meromorphic function, approximation
Received by editor(s): July 25, 2002
Published electronically: June 25, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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