On Davenport's bound for the degree of f³ - g² and Riemann's Existence Theorem

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1. [BCHS] B. J. Birch, S. Chowla, M. Hall, Jr., and A. Schinzel, On the difference x³-y², Norske Vid. Selsk. Forh. (Trondheim) 38 (1965), 65-69. 
2. [B-M] W. D. Brownawell and D. Masser, Vanishing sums in function fields, Math. Proc. Cambridge Philos. Soc. 100 (1986), 427-434. Zbl0612.10010
3. [Ca-Fr] J. W. S. Cassels and A. Fröhlich, Algebraic Number Theory, Academic Press, 1967. 
4. [Ch] B. Chiarellotto, On Lamé operators with finite monodromy group, Trans. Amer. Math. Soc., to appear. 
5. [CMK] M. Conder and J. McKay, A necessary condition for transitivity of a finite permutation group, Bull. London Math. Soc. 20 (1988), 235-238. Zbl0663.20003
6. [Dan] L. Danilov, Letter to the editor, Mat. Zametki 36 (1971), 103-107 (in Russian). 
7. [Dav] H. Davenport, On f³(t) - g²(t), Norske Vid. Selsk. Forh. (Trondheim) 38 (1965), 86-87. 
8. [FLS] W. Feit, R. Lyndon and L. L. Scott, A remark about permutations, J. Combin. Theory Ser. A 18 (1975), 234-235. Zbl0297.05021
9. [Fr1] M. Fried, On a conjecture of Schur, Michigan Math. J. 17 (1970), 41-55. 
10. [Fr2] M. Fried, Fields of definition of function fields and Hurwitz families - Groups as Galois groups, Comm. Algebra 5 (1977), 17-82. Zbl0478.12006
11. [Fu] W. Fulton, The fundamental group of a curve, Archives of the Princeton Mathematical Library, 1966. 
12. [Gr] A. Grothendieck, Esquisse d'un programme, preprint, 1984. 
13. [Ha] M. Hall, Jr., The Diophantine equation x³ - y² = k, in: Computers in Number Theory, A. O. L. Atkin and B. J. Birch (eds.), Proc. Oxford 1969, Academic Press, 1971, 173-198. 
14. [Har] F. Harary, Graph Theory, 3rd ed., Addison Wesley, 1972. 
15. [J-S] G. Jones and D. Singerman, Maps, hypermaps and triangle groups, preprint Univ. of Southampton, July 1993. Zbl0833.20045
16. [Lang] S. Lang, Number Theory III, Encyclopaedia Math. Sci. 60, Springer, 1991. Zbl0744.14012
17. [La] M. Langevin, Cas d'égalité pour le Théorème de Mason et applications de la conjecture (abc), C. R. Acad. Sci. Paris 317 (1993), 441-444. 
18. [Ma] R. C. Mason, Diophantine Equations over Function Fields, London Math. Soc. Lecture Note Ser. 96, Cambridge Univ. Press, 1984. Zbl0533.10012
19. [Ree] R. Ree, A theorem on permutations, J. Combin. Theory Ser. A 10 (1971), 174-175. Zbl0221.05033
20. [Se1] J. P. Serre, Topics in Galois Theory, Course at Harvard University, Fall 1988 (Notes by H. Darmon). 
21. [Se2] J. P. Serre, Corps locaux, Hermann, Paris, 1968. 
22. [S-V] G. B. Shabat and V. A. Voevodsky, Drawing curves over number fields, in: The Grothendieck Festschrift, vol. III, Progr. Math. 88, Birkhäuser, 1990, 199-227. Zbl0790.14026
23. [Sie] W. Sierpiński, Elementary Theory of Numbers, edited by A. Schinzel, 2nd ed., North-Holland, 1988. 
24. [Sin] D. Singerman, Subgroups of Fuchsian groups and finite permutation groups, Bull. London Math. Soc. 2 (1970), 319-323. Zbl0206.30804
25. [Tr] M. Tretkoff, Algebraic extensions of the field of rational functions, Comm. Pure Appl. Math. 24 (1971), 491-497. Zbl0226.12101
26. [U-Y] S. Uchiyama and M. Yorinaga, On the difference f³(x)-g²(x), Tsukuba J. Math. 6 (1982), 215-230. Zbl0526.12013
27. [Vo] P. Vojta, Diophantine Approximation and Value Distribution Theory, Lecture Notes in Math. 1239, Springer, 1987. Zbl0609.14011
28. [Wie] H. Wielandt, Finite Permutation Groups, Academic Press, New York, 1964. Zbl0138.02501
29. [Za] U. Zannier, Some remarks on the S-unit equation in function fields, Acta Arith. 64 (1993), 87-98. Zbl0786.11019

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