Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Unique range sets and uniqueness polynomials for algebraic curves


Authors: Ta Thi Hoai An and Julie Tzu-Yueh Wang
Journal: Trans. Amer. Math. Soc. 359 (2007), 937-964
MSC (2000): Primary 14H05; Secondary 30D35, 14H55
DOI: https://doi.org/10.1090/S0002-9947-06-04018-9
Published electronically: October 16, 2006
MathSciNet review: 2262838
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study unique range sets and uniqueness polynomials for algebraic functions on a smooth projective algebraic curve over an algebraically closed field of characteristic zero.


References [Enhancements On Off] (What's this?)

  • 1. T. T. H. AN AND J. T.-Y. WANG, Uniqueness polynomials for complex meromorphic functions, Inter. J. Math. 13 No. 10 (2002), 1095-1115. MR 1945708 (2003i:30040)
  • 2. T. T. H. AN AND J. T.-Y. WANG, A note on uniqueness polynomials for complex entire functions, preprint.
  • 3. T. T. H. AN, J. T.-Y. WANG, AND P.-M. WONG, Strong uniqueness polynomials: the complex case, Journal of Complex Variables and its Application 49 No. 1 (2004), 25-54. MR 2031025 (2004j:30054)
  • 4. T. T. H. AN, J. T.-Y. WANG, AND P.-M. WONG, Unique range sets and uniqueness polynomials in positive characteristic II, Acta Arith. 116 (2005), 115-143. MR 2110391 (2005k:12002)
  • 5. R. M. AVANZI AND U. M. ZANNIER, The equation $ f(X)=f(Y)$ in rational functions $ X=X(t)$, $ Y=Y(t)$, Compositio Math. 139 (2003), 263-295. MR 2041613 (2004m:14057)
  • 6. W. CHERRY AND J. T.-Y. WANG, Uniqueness polynomials for entire functions, Inter. J. Math 13 No. 3 (2002), 323-332. MR 1911106 (2003d:30033)
  • 7. G. FALTINGS, Endlichkeitssatze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), 349-366. MR 0718935 (85g:11026a)
  • 8. H. FUJIMOTO, On uniqueness of meromorphic functions sharing finite sets, Amer. J. Math. 122 (2000), 1175-1203. MR 1797660 (2001k:30040)
  • 9. F. GROSS, Factorization of meromorphic functions and some open problems in complex analysis, Proc. Conf. Univ. Kentucky, Lexington, KY, 1976, Lecture Notes in Math. 599, Springer-Verlag, 1977. MR 0450529 (56:8823)
  • 10. G. GUNDERSEN, Meromorphic functions sharing four values, Trans. Amer. Math. Soc. 277 (1983), 545-567. MR 0694375 (84g:30028)
  • 11. A. SAUER, Uniqueness theorems for holomorphic functions on compact Riemann surfaces, New Zealand J. Math. 30 (2001), 177-181. MR 1877545 (2002k:30078)
  • 12. A. SCHWEIZER, Shared values of meromorphic functions on compact Riemann surfaces, Arch. Math. (Basel) 84 (2005), 71-78. MR 2106406 (2005k:30063)
  • 13. J. T.-Y. WANG, Uniqueness polynomials and bi-unique range sets for rational functions and non-Archimedean meromorphic functions, Acta Arith. 104 (2002), 183-200. MR 1914252 (2003h:12002)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14H05, 30D35, 14H55

Retrieve articles in all journals with MSC (2000): 14H05, 30D35, 14H55


Additional Information

Ta Thi Hoai An
Affiliation: Institute of Mathematics, Academia Sinica, Nankang, Taipei 11529, Taiwan, R.O.C.
Address at time of publication: Institute of Mathematics, 18 Hoang Quoc Viet Road, Cau Giay District, 10307 Hanoi, Vietnam
Email: antu_inp@yahoo.fr

Julie Tzu-Yueh Wang
Affiliation: Institute of Mathematics, Academia Sinica, Nankang, Taipei 11529, Taiwan, R.O.C.
Email: jwang@math.sinica.edu.tw

DOI: https://doi.org/10.1090/S0002-9947-06-04018-9
Received by editor(s): September 4, 2004
Published electronically: October 16, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society