Geodesic
Diophantine equations over function fields
Sbornik. Mathematics, Tome 40 (1981) no. 1, pp. 79-85 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{SM_1981_40_1_a3,
     author = {S. A. Stepanov},
     title = {Diophantine equations over function fields},
     journal = {Sbornik. Mathematics},
     pages = {79--85},
     year = {1981},
     volume = {40},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1981_40_1_a3/}
}
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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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[4] W. M. Schmidt, “Thue's equation over function fields”, J. Australian Math. Soc., Ser. A, 25:4 (1978), 385–422 | DOI | MR | Zbl