The strength of Cartan's version of nevanlinna theory

Bulletin of the London Mathematical Society

Volumn 36, Issue 4, 2004, Pages 433-454

  Gundersen, Gary G ^a   Hayman, Walter K ^b  

^a UNIVERSITY OF NEW ORLEANS   (United States)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3142689610     PISSN: 00246093     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024609304003418     Document Type: Review

References (49)

1. I. N. BAKER, 'On a class of meromorphic functions', Proc. Amer. Math. Soc. 17 (1966) 819-822.
2. H. CARTAN, 'Sur les zéros des combinaisons linéaires de p fonctions holomorphes données', Mathematica Cluj 7 (1933) 5-31.
3. A. E. EREMENKO and M. L. SODIN, 'The value distribution of meromorphic functions and meromorphic curves from the point of view of potential theory', Algebra i Analiz 3 (1991) 131-164 (in Russian); translation in St. Petersburg Math. J. 3 (1992) 109-136.
4. A. E. EREMENKO and M. L. SODIN, 'The value distribution of meromorphic functions and meromorphic curves from the point of view of potential theory', Algebra i Analiz 3 (1991) 131-164 (in Russian); translation in St. Petersburg Math. J. 3 (1992) 109-136.
5. H. FUJIMOTO, 'On meromorphic maps into the complex projective space', J. Math. Soc. Japan 26 (1974) 272-288.
6. A. GRANVILLE and T. J. TUCKER, 'It's as easy as abc', Notices Amer. Math. Soc. 49 (2002) 1224-1231.
7. M. L. GREEN, 'Some Picard theorems for holomorphic maps to algebraic varieties', Amer. J. Math. 97 (1975) 43-75.
8. n = 1', Bull. Amer. Math. Soc. 72 (1966) 86-88. Correction: ibid. 72 (1966) 576.
9. n and a new approach to a certain class of more general functional equations', Indian J. Math. 23 (1981) 17-39.
10. 6 ≡ 1', Analysis 18 (1998) 285-290.
11. 5 ≡ 1', Complex Variables 43 (2001) 293-298.
12. G. G. GUNDERSEN, 'Complex functional equations', Complex differential and functional equations (Mekrijärvi, 2000). Univ. Joensuu Dept. Math. Rep. Ser. 5 (Univ. Joensuu, Joensuu, 2003) 21-50.
13. G. G. GUNDERSEN and K. TOHGE, 'Unique range sets for polynomials or rational functions', Progress in Analysis, Proc. 3rd ISSAC Congress, vol. 1 (ed. H. G. W. Begehr, R. P. Gilbert and M. W. Wong, World Scientific, 2003) 235-246.
14. 5 = 1', Univ. Joensuu Dept. Math. Rep. Ser., to appear.
15. W. K. HAYMAN, Meromorphic functions (Clarendon Press, Oxford, 1964).
16. W. K. HAYMAN, Research problems in function theory (Athlone Press, University of London, 1967).
17. W. K. HAYMAN, 'Rolf Nevanlinna', Bull. London Math. Soc. 14 (1982) 419-436.
18. W. K. HAYMAN, 'Waring's problem für analytische Funktionen', Bayer. Akad. Wiss. Math.-Natur. Kl Sitzungsber. 1984 (Bayer. Akad. Wiss., Munich, 1985) 1-13.
19. D. HILBERT, 'Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl n-ter Potenzen (Waringsches Problem)', Math. Ann. 67 (1909) 281-300.
20. P.-C. Hu and C.-C. YANG, 'A generalized abc-conjecture over function fields', J. Number Theory 94 (2002) 286-298.
21. P.-C. Hu and C.-C. YANG, 'A note on the abc conjecture', Comm. Pure Applied Math. vol. LV (2002) 1089-1103.
22. X.-H. HUA and C.-C. YANG, 'Uniqueness problems of entire and meromorphic functions', Bull Hong Kong Math. Soc. 1 (1997) 289-300.
23. G. IYER, 'On certain functional equations', J. Indian Math. Soc. 3 (1939) 312-315.
24. D.-I. KIM, 'Waring's problem for linear polynomials and Laurent polynomials', Rocky Mountain J. Math., to appear.
25. I. LAINE, Nevanlinna theory and complex differential equations (Walter de Gruyter, Berlin/New York, 1993).
26. S. LANG, Introduction to complex hyperbolic spaces (Springer, New York, 1987).
27. S. LANG, 'Old and new conjectured diophantine inequalities', Bull. Amer. Math. Soc. 23 (1990) 37-75.
28. S. LANG, Algebra, revised 3rd edn (Springer, New York, 2002).
29. O. LEHTO, 'On the birth of the Nevanlinna theory', Ann. Acad. Sci. Fenn. Math. 7 (1982) 5-23.
30. P. Li and C.-C. YANG, 'Some further results on the unique range sets of meromorphic functions', Kodai Math. J. 18 (1995) 437-450.
31. R. C. MASON. Diophantine equations over function fields, London Math. Soc. Lecture Note Series 96 (Cambridge Univ. Press, 1984).
32. R. C. MASON, Equations over function fields, Lecture Notes in Math. 1068 (Springer, Berlin/New York, 1984) 149-157.
33. J. MOLLUZZO, 'Monotonicity of quadrature formulas and polynomial representation', Doctoral thesis, Yeshiva University, 1972.
34. E. MUES, 'Shared value problems for meromorphic functions', Value distribution theory and complex differential equations (Joensuu, 1994), Univ. Joensuu Publications in Sciences 35 (1995) 17-43.
35. E. MUES and M. REINDERS, 'Meromorphic functions sharing one value and unique range sets', Kodai Math. J. 18 (1995) 515-522.
36. M. B. NATHANSON, Elementary methods in number theory (Springer, New York, 2000).
37. R. NEVANLINNA, 'Zur Theorie der meromorphen Funktionen', Acta Math. 46 (1925) 1-99.
38. R. NEVANLINNA, Le théorème de Picard-Borel et la théorie des fonctions méromorphes (Gauthier-Villars, Paris, 1929).
39. D. J. NEWMAN and M. SLATER, 'Waring's problem for the ring of polynomials', J. Number Theory 11 (1979) 477-487.
40. B. REZNICK, 'Patterns of dependence among powers of polynomials', Algorithmic and quantitative real algebraic geometry, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 60 (Amer. Math. Soc., Providence, RI, 2003) 101-121.
41. B. SHIFFMAN, 'Uniqueness of entire and meromorphic functions sharing finite sets', Complex Variables 43 (2001) 433-449.
42. M. SHIROSAKI, 'On polynomials which determine holomorphic mappings', J. Math. Soc. Japan 49 (1997) 289-298.
43. W. W. STOTHERS, 'Polynomial identities and Hauptmoduln', Quart. J. Math. Oxford (2) 32 (1981) 349-370.
44. R. TAYLOR and A. WILES, 'Ring-theoretic properties of certain Hecke algebras', Ann. of Math. 141 (1995) 553-572.
45. ni = 1', Tôhoku Math. J. 23 (1971) 289-299.
46. H. WEYL (in collaboration with F. J. WEYL), Meromorphic functions and analytic curves (Princeton Univ. Press, Princeton, NJ, 1943).
47. A. WILES, 'Modular elliptic curves and Fermat's last theorem', Ann. of Math. 141 (1995) 443-551.
48. L. YANG, Value distribution theory, revised edition of the original Chinese edition (Springer, Berlin, 1993).
49. H.-X. YI, 'The unique range sets for entire or meromorphic functions', Complex Variables 28 (1995) 13-21.