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Volumn 487, Issue , 1997, Pages 61-83

Nevanlinna-Cartan theory over function fields and a Diophantine equation

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EID: 0031461665     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (16)

References (49)
  • 1
    • 0000150833 scopus 로고
    • The generalized fermat equation in function fields
    • E. Bombieri and J. Mueller, The generalized Fermat equation in function fields, J. Number Th. 39 (1991), 339-350.
    • (1991) J. Number Th. , vol.39 , pp. 339-350
    • Bombieri, E.1    Mueller, J.2
  • 3
    • 0002450217 scopus 로고
    • Sur les zéros des combinaisons linéaires de p fonctions holomorphes données
    • H. Cartan, Sur les zéros des combinaisons linéaires de p fonctions holomorphes données, Mathematica 7 (1933), 5-31.
    • (1933) Mathematica , vol.7 , pp. 5-31
    • Cartan, H.1
  • 4
    • 84966219423 scopus 로고
    • Defect relations for degenerate meromorphic maps
    • W. Chen, Defect relations for degenerate meromorphic maps, Trans. Amer. Math. Soc. 319 (1990), 499-515.
    • (1990) Trans. Amer. Math. Soc. , vol.319 , pp. 499-515
    • Chen, W.1
  • 5
    • 0000252436 scopus 로고
    • Diophantine approximation on Abelian varieties
    • G. Faltings, Diophantine approximation on Abelian varieties, Ann. Math. 133 (1991), 549-576.
    • (1991) Ann. Math. , vol.133 , pp. 549-576
    • Faltings, G.1
  • 8
    • 0002103191 scopus 로고
    • On the numbers of families of solutions of systems of decomposable form equations
    • K. Györy, On the numbers of families of solutions of systems of decomposable form equations, Publ. Math. Debrecen 42 (1993), 65-101.
    • (1993) Publ. Math. Debrecen , vol.42 , pp. 65-101
    • Györy, K.1
  • 10
    • 0009224093 scopus 로고
    • A finiteness theorem for holomorphic families of Riemann surfaces
    • D. Drasin (ed.), Springer, New York-Berlin-Heidelberg-London-Paris-Tokyo
    • Y. Imayoshi and H. Shiga, A finiteness theorem for holomorphic families of Riemann surfaces, in: D. Drasin (ed.), Holomorphic Functions and Moduli vol. II, Springer, New York-Berlin-Heidelberg-London-Paris-Tokyo 1988.
    • (1988) Holomorphic Functions and Moduli , vol.2
    • Imayoshi, Y.1    Shiga, H.2
  • 11
    • 0000621162 scopus 로고
    • p-Adic Nevanlinna-Cartan theorem
    • H.H. Khoai and M.V. Tu, p-adic Nevanlinna-Cartan theorem, Internat. J. Math. 6 (1995), 719-731.
    • (1995) Internat. J. Math. , vol.6 , pp. 719-731
    • Khoai, H.H.1    Tu, M.V.2
  • 12
    • 0010756161 scopus 로고
    • Hyperbolic manifolds and holomorphic mappings
    • Marcel Dekker, New York
    • S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Pure Appl. Math. 2, Marcel Dekker, New York 1970.
    • (1970) Pure Appl. Math. , vol.2
    • Kobayashi, S.1
  • 13
    • 84968502581 scopus 로고
    • Intrinsic distances, measures, and geometric function theory
    • S. Kobayashi, Intrinsic distances, measures, and geometric function theory, Bull. Amer. Math. Soc. 82 (1976), 357-416.
    • (1976) Bull. Amer. Math. Soc. , vol.82 , pp. 357-416
    • Kobayashi, S.1
  • 14
    • 84968473107 scopus 로고
    • Higher dimensional diophantine problems
    • S. Lang, Higher dimensional Diophantine problems, Bull. Amer. Math. Soc. 80 (1974), 779-787.
    • (1974) Bull. Amer. Math. Soc. , vol.80 , pp. 779-787
    • Lang, S.1
  • 15
    • 84968488143 scopus 로고
    • Hyperbolic and diophantine analysis
    • S. Lang, Hyperbolic and Diophantine analysis, Amer. Math. Soc. 14 (1986), 159-205.
    • (1986) Amer. Math. Soc. , vol.14 , pp. 159-205
    • Lang, S.1
  • 17
    • 0003360933 scopus 로고
    • Number theory III
    • Springer-Verlag. Berlin-Heidelberg-New York-London-Paris-Tokyo-Hong Kong-Barcelona
    • S. Lang, Number Theory III, Encycl. Math. Sci. 60, Springer-Verlag. Berlin-Heidelberg-New York-London-Paris-Tokyo-Hong Kong-Barcelona 1991.
    • (1991) Encycl. Math. Sci. , vol.60
    • Lang, S.1
  • 18
    • 0000309927 scopus 로고
    • Equations diophantines exponentielles
    • M. Laurent, Equations diophantines exponentielles, Invent. Math. 78 (1984). 299-327.
    • (1984) Invent. Math. , vol.78 , pp. 299-327
    • Laurent, M.1
  • 19
    • 0001063255 scopus 로고
    • Zur approximation algebraischer zahlen, I. (über den größten primteiler binärer formen)
    • K. Mahler, Zur Approximation algebraischer Zahlen, I. (Über den größten Primteiler binärer Formen), Math. Ann. 107 (1933), 691-730.
    • (1933) Math. Ann. , vol.107 , pp. 691-730
    • Mahler, K.1
  • 20
    • 0003303826 scopus 로고
    • Diophantine equations over function fields
    • Cambridge University Press, Cambridge
    • R.C. Mason, Diophantine Equations over Function Fields, London Math. Soc. Lect. Notes 96, Cambridge University Press, Cambridge 1984.
    • (1984) London Math. Soc. Lect. Notes , vol.96
    • Mason, R.C.1
  • 21
    • 38249042545 scopus 로고
    • Norm form equations, I
    • R.C. Mason, Norm form equations, I, J. Number Th. 22 (1986), 190-207.
    • (1986) J. Number Th. , vol.22 , pp. 190-207
    • Mason, R.C.1
  • 23
    • 0000615881 scopus 로고
    • Binomial thue's equation over function fields
    • J. Mueller, Binomial Thue's equation over function fields, Comp. Math. 73 (1990), 189-197.
    • (1990) Comp. Math. , vol.73 , pp. 189-197
    • Mueller, J.1
  • 24
    • 0010761737 scopus 로고
    • The nonexistence of certain level structures on abelian varieties over complex function fields
    • A.M. Nadel, The nonexistence of certain level structures on abelian varieties over complex function fields, Ann. Math. 129 (1989), 161-178.
    • (1989) Ann. Math. , vol.129 , pp. 161-178
    • Nadel, A.M.1
  • 25
    • 0000973537 scopus 로고
    • On the theory of meromorphic functions
    • E.I. Nochka, On the theory of meromorphic functions, Sov. Math. Dokl. 27 (1983), 377-381.
    • (1983) Sov. Math. Dokl. , vol.27 , pp. 377-381
    • Nochka, E.I.1
  • 26
    • 0001379622 scopus 로고
    • A higher dimensional analogue of Mordell's conjecture over function fields
    • J. Noguchi, A higher dimensional analogue of Mordell's conjecture over function fields, Math. Ann. 258 (1981), 207-212.
    • (1981) Math. Ann. , vol.258 , pp. 207-212
    • Noguchi, J.1
  • 27
    • 85008542606 scopus 로고
    • Hyperbolic fibre spaces and Mordell's conjecture over function fields
    • J. Noguchi, Hyperbolic fibre spaces and Mordell's conjecture over function fields, Publ. RIMS, Kyoto Univ. 21 (1985), 27-46.
    • (1985) Publ. RIMS, Kyoto Univ. , vol.21 , pp. 27-46
    • Noguchi, J.1
  • 28
    • 0002191597 scopus 로고
    • Hyperbolic manifolds and diophantine geometry
    • Amer. Math. Soc., Providence, Rhode Island
    • J. Noguchi, Hyperbolic manifolds and Diophantine geometry, Sugaku Expos. 4 (1991), 63-81, Amer. Math. Soc., Providence, Rhode Island.
    • (1991) Sugaku Expos. , vol.4 , pp. 63-81
    • Noguchi, J.1
  • 29
    • 0010677323 scopus 로고
    • Moduli space of Abelian varieties with level structure over function fields
    • J. Noguchi, Moduli space of Abelian varieties with level structure over function fields, Internat. J. Math. 2 (1991), 183-194.
    • (1991) Internat. J. Math. , vol.2 , pp. 183-194
    • Noguchi, J.1
  • 30
    • 0000852944 scopus 로고
    • Meromorphic mappings into compact hyperbolic complex spaces and geometric diophantine problem
    • J. Noguchi, Meromorphic mappings into compact hyperbolic complex spaces and geometric Diophantine problem, Internat. J. Math. 3 (1992), 277-289.
    • (1992) Internat. J. Math. , vol.3 , pp. 277-289
    • Noguchi, J.1
  • 31
    • 0010678150 scopus 로고
    • An example of a hyperbolic fiber space without hyperbolic embedding into compactification
    • Proc. Osaka International Conference, Osaka 1990, Complex Geometry (G. Komatsu and Y. Sakane, eds.), Marcel Dekker, New York-Basel-Hong Kong
    • J. Noguchi, An example of a hyperbolic fiber space without hyperbolic embedding into compactification, Proc. Osaka International Conference, Osaka 1990, Complex Geometry (G. Komatsu and Y. Sakane, eds.), Lect. Notes Pure Appl. Math. 143 (1993), 157-160, Marcel Dekker, New York-Basel-Hong Kong.
    • (1993) Lect. Notes Pure Appl. Math. , vol.143 , pp. 157-160
    • Noguchi, J.1
  • 32
    • 0010675601 scopus 로고
    • Some topics in Nevanlinna theory, hyperbolic manifolds and diophantine geometry
    • Festschrift for S. Kobayashi 60th Birthday, World Scientific, Singapore
    • J. Noguchi, Some topics in Nevanlinna theory, hyperbolic manifolds and Diophantine geometry. Geometry and Analysis on Complex Manifold, Festschrift for S. Kobayashi 60th Birthday, pp. 140-156, World Scientific, Singapore 1994.
    • (1994) Geometry and Analysis on Complex Manifold , pp. 140-156
    • Noguchi, J.1
  • 33
    • 0003310574 scopus 로고
    • Geometric function theory in several complex variables
    • Amer. Math. Soc., Providence, Rhode Island
    • J. Noguchi and T. Ochiai, Geometric Function Theory in Several Complex Variables, Transl. Math. Monogr. 80, Amer. Math. Soc., Providence, Rhode Island, 1990.
    • (1990) Transl. Math. Monogr. , vol.80
    • Noguchi, J.1    Ochiai, T.2
  • 34
    • 0010675602 scopus 로고
    • Exponential diophantine equations over function fields
    • Â. Pintér, Exponential diophantine equations over function fields, Publ. Math. Debrecen 41 (1992), 89-98.
    • (1992) Publ. Math. Debrecen , vol.41 , pp. 89-98
    • Pintér, A.1
  • 35
    • 0010677324 scopus 로고
    • Around the Mordell conjecture for function fields and a conjecture of S. Lang, algebraic geometry
    • (M. Raynaud and T. Shioda, eds.), Springer, Berlin-New York
    • M. Raynaud, Around the Mordell conjecture for function fields and a conjecture of S. Lang, Algebraic Geometry (M. Raynaud and T. Shioda, eds.), Lect. Notes Math. 1016 (1983), 1-19, Springer, Berlin-New York.
    • (1983) Lect. Notes Math. , vol.1016 , pp. 1-19
    • Raynaud, M.1
  • 37
    • 0000598865 scopus 로고
    • The p-adic Thue-Siegel-Roth-Schmidt theorem
    • H.P. Schlickewei, The p-adic Thue-Siegel-Roth-Schmidt Theorem, Arch. Math. 29 (1977), 267-270.
    • (1977) Arch. Math. , vol.29 , pp. 267-270
    • Schlickewei, H.P.1
  • 38
    • 0003304303 scopus 로고
    • Diophantine approximation
    • Springer, Berlin-Heidelberg-New York
    • W. Schmidt, Diophantine Approximation, Lect. Notes Math. 785, Springer, Berlin-Heidelberg-New York 1980.
    • (1980) Lect. Notes Math. , vol.785
    • Schmidt, W.1
  • 39
    • 0003267223 scopus 로고
    • Diophantine approximations and diophantine equations
    • Springer, Berlin-Heidelberg-New York
    • W. Schmidt, Diophantine Approximations and Diophantine Equations, Lect. Notes Math. 1467, Springer, Berlin-Heidelberg-New York 1991.
    • (1991) Lect. Notes Math. , vol.1467
    • Schmidt, W.1
  • 41
    • 84968515665 scopus 로고
    • The Catalan equation over function fields
    • J.H. Silverman, The Catalan equation over function fields, Trans. Amer. Math. Soc. 273 (1982), 201-205.
    • (1982) Trans. Amer. Math. Soc. , vol.273 , pp. 201-205
    • Silverman, J.H.1
  • 42
    • 84972572617 scopus 로고
    • Moduli spaces of holomorphic mappings into hyperbolically embedded complex spaces and holomorphic fibre spaces
    • M. Suzuki, Moduli spaces of holomorphic mappings into hyperbolically embedded complex spaces and holomorphic fibre spaces, J. Math. Soc. Japan 46 (1994), 681-698.
    • (1994) J. Math. Soc. Japan , vol.46 , pp. 681-698
    • Suzuki, M.1
  • 43
    • 84972552028 scopus 로고
    • Mordell property of hyperbolic fiber spaces with noncompact fibers
    • M. Suzuki, Mordell property of hyperbolic fiber spaces with noncompact fibers, Tôhoku Math. J. 47 (1995), 601-611.
    • (1995) Tôhoku Math. J. , vol.47 , pp. 601-611
    • Suzuki, M.1
  • 44
    • 0003341672 scopus 로고
    • Diophantine approximations and value distribution theory
    • Springer, Berlin-Heidelberg-New York
    • P. Vojta, Diophantine Approximations and Value Distribution Theory, Lect. Notes Math. 1239, Springer, Berlin-Heidelberg-New York 1987.
    • (1987) Lect. Notes Math. , vol.1239
    • Vojta, P.1
  • 45
    • 51249176294 scopus 로고
    • Diagonal equations over function fields
    • J.F. Voloch, Diagonal equations over function fields, Bol. Soc. Brasil. Math. 16 (1985), 29-39.
    • (1985) Bol. Soc. Brasil. Math. , vol.16 , pp. 29-39
    • Voloch, J.F.1
  • 47
    • 0030140921 scopus 로고    scopus 로고
    • The truncated second main theorem of function fields
    • J.T.-Y. Wang, The truncated second main theorem of function fields, J. Number Th. 58 (1996), 139-157.
    • (1996) J. Number Th. , vol.58 , pp. 139-157
    • Wang, J.T.-Y.1
  • 48
    • 0030366414 scopus 로고    scopus 로고
    • Effective roth theorem of function fields
    • J.T.-Y. Wang, Effective Roth theorem of function fields, Rocky Mountain J. Math. 26 (1996). 1225-1234.
    • (1996) Rocky Mountain J. Math. , vol.26 , pp. 1225-1234
    • Wang, J.T.-Y.1
  • 49
    • 0010761739 scopus 로고
    • A function-field analog of the Mordell conjecture: A noncompact version
    • M.G. Zaidenberg, A function-field analog of the Mordell conjecture: a noncompact version, Math. USSR Izvest. 35 (1990), 61-81.
    • (1990) Math. USSR Izvest. , vol.35 , pp. 61-81
    • Zaidenberg, M.G.1


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