Hu, Pei-Chu; Yang, Chung-Chun A generalized \(abc\)-conjecture over function fields. (English) Zbl 1007.11015 J. Number Theory 94, No. 2, 286-298 (2002). The authors suggest a generalised version of the \(abc\)-conjecture, in fact a sharpened \(a_0a_1\ldots a_k\)-conjecture, and provide an instructive proof of its analogue for non-Archimedean entire functions as well as of a sharpened generalisation of Mason’s theorem for polynomials. Reviewer: A.J.van der Poorten (Macquarie) Cited in 2 ReviewsCited in 5 Documents MSC: 11D88 \(p\)-adic and power series fields 12J25 Non-Archimedean valued fields 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30G06 Non-Archimedean function theory Keywords:non-Archimedean entire functions; Mason’s theorem for polynomials PDFBibTeX XMLCite \textit{P.-C. Hu} and \textit{C.-C. Yang}, J. Number Theory 94, No. 2, 286--298 (2002; Zbl 1007.11015) Full Text: DOI References: [1] Browkin, J.; Brzeziński, J., Some remarks on the abc-conjecture, Math. Comput., 62, 931-939 (1994) · Zbl 0804.11006 [2] Davenport, H., On \(f^3(t)\)−\(g^2(t)\), Norske Vid. Selsk. Forh. (Trondheim), 38, 86-87 (1965) · Zbl 0136.25204 [3] Escassut, A., Analytic Elements in \(p\)-adic Analysis (1995), World Scientific: World Scientific Singapore · Zbl 0933.30030 [4] Hu, P. C.; Yang, C. C., Value distribution theory of \(p\)-adic meromorphic functions, Izv. Nats. Acad. Nauk Armenii, 32, 46-67 (1997) · Zbl 0954.30030 [5] Hu, P. C.; Yang, C. C., The “abc” conjecture over function fields, Proc. Japan Acad. Ser. A, 76, 118-120 (2000) · Zbl 0979.11023 [6] Hu, P. C.; Yang, C. C., Meromorphic Functions over Non-Archimedean Fields. Meromorphic Functions over Non-Archimedean Fields, Mathematics and Its Applications, 522 (2000), Kluwer Academic: Kluwer Academic Dordrecht · Zbl 0984.30027 [7] Lang, S., Old and new conjectured Diophantine inequalities, Bull. Amer. Math. Soc., 23, 37-75 (1990) · Zbl 0714.11034 [8] Mason, R. C., Equations over Function Fields. Equations over Function Fields, Lecture Notes in Mathematics, 1068 (1984), Springer-Verlag: Springer-Verlag Berlin/New York, p. 149-157 · Zbl 0544.10015 [9] Mason, R. C., Diophantine Equations over Function Fields. Diophantine Equations over Function Fields, London Math. Soc. Lecture Note Series, 96 (1984), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0533.10012 [10] Mason, R. C., The hyperelliptic equation over function fields, Math. Proc. Cambridge Philos. Soc., 93, 219-230 (1983) · Zbl 0513.10016 [11] Nevanlinna, R., Le théorème de Picard-Borel et la théorie des fonctions méromorphes (1929), Gauthier-Villars: Gauthier-Villars Paris · JFM 55.0773.03 [12] Schmidt, W. M., Diophantine Approximations and Diophantine Equations. Diophantine Approximations and Diophantine Equations, Lecture Notes in Mathematics, 1467 (1991), Springer-Verlag: Springer-Verlag Berlin/New York · Zbl 0754.11020 [13] Shapiro, H. N.; Sparer, G. H., Extension of a theorem of Mason, Comm. Pure Appl. Math., 47, 711-718 (1994) · Zbl 0818.11019 [14] Stothers, W. W., Polynomial identities and Hauptmoduln, Quart. J. Math. Oxford Ser. (2), 32, 349-370 (1981) · Zbl 0466.12011 [15] van Frankenhuysen, M., Hyperbolic Spaces and the abc Conjecture (1995), Katholieke Universiteit Nijmegen [16] Vojta, P., Diophantine Approximation and Value Distribution Theory. Diophantine Approximation and Value Distribution Theory, Lecture Notes in Mathematics, 1239 (1987), Springer-Verlag: Springer-Verlag Berlin/New York · Zbl 0609.14011 [17] Voloch, J. F., Diagonal equations over function fields, Bol. Soc. Brasil. Mat., 16, 29-39 (1985) · Zbl 0612.10011 [18] Zannier, U., Some remarks on the \(S\)-unit equation in function fields, Acta Arith., 64, 87-98 (1993) · Zbl 0786.11019 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.