Mahler, Kurt

Reprint: Über die rationalen Punkte auf Kurven vom Geschlecht Eins (1934)

Doc. Math. Extra Vol. Mahler Selecta, 387-398 (2019)
DOI: 10.25537/dm.2019.SB-387-398


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)].

Mathematics Subject Classification

11-03, 11D41, 11G99, 14G05, 14H25