Geodesic
Reprint: Über die rationalen Punkte auf Kurven vom Geschlecht Eins (1934)
Documenta mathematica, Mahler Selecta (2019), pp. 387-398.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $f(x,y)$ be an irreducible polynomial with rational coefficients and suppose that $f(x,y)=0$ defines a curve of genus one with infinitely many rational points $(x,y)$ lying on it. In this paper, Mahler shows that given a finite set $S$ of prime numbers, there are only finitely many rational points $(x, y)$ on the curve such that $x$ or $y$ has all its prime factors in $S$. \par Reprint of the author's paper [J. Reine Angew. Math. 170, 168--178 (1934; Zbl 0008.20002; JFM 60.0159.03)].
Classification : 11-03, 11D41, 11G99, 14G05, 14H25 
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     author = {Mahler, Kurt},
     title = {Reprint: {\"Uber} die rationalen {Punkte} auf {Kurven} vom {Geschlecht} {Eins} (1934)},
     journal = {Documenta mathematica},
     pages = {387--398},
     publisher = {mathdoc},
     volume = {Mahler Selecta},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__S1__a21/}
}
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Mahler, Kurt. Reprint: Über die rationalen Punkte auf Kurven vom Geschlecht Eins (1934). Documenta mathematica, Mahler Selecta (2019), pp. 387-398. http://geodesic.mathdoc.fr/item/DOCMA_2019__S1__a21/