Geodesic
Diophantine equations over function fields
Sbornik. Mathematics, Tome 40 (1981) no. 1, pp. 79-85 
S. A. Stepanov. Diophantine equations over function fields. Sbornik. Mathematics, Tome 40 (1981) no. 1, pp. 79-85. http://geodesic.mathdoc.fr/item/SM_1981_40_1_a3/
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     title = {Diophantine equations over function fields},
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper proves the boundedness of the degrees of at least two components of an arbitrary solution $(x_1,\dots,x_n)$ of the equation $$ a_1x_1^{s_1}+\dots+a_nx_n^{s_n}=0, $$ where $x_1(t),\dots,x_n(t)$ are pairwise relatively prime polynomials. Bibliography: 4 titles.

[1] S. Uchiyama, “Rational approximation to algebraic functions”, J. Fac. Sci. Hokkaido Univ., Ser. 1, 15 (1961), 173–192 | MR | Zbl

[2] Yu. I. Manin, “Ratsionalnye tochki algebraicheskikh krivykh nad funktsionalnymi polyami”, Izv. AN SSSR, seriya matem., 27 (1963), 1395–1440 | MR

[3] H. Grauert, “Mordells Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörper”, Inst. Haut. Etudes, 25 (1965), 131–149 | DOI | MR

[4] W. M. Schmidt, “Thue's equation over function fields”, J. Australian Math. Soc., Ser. A, 25:4 (1978), 385–422 | DOI | MR | Zbl