Mahler, Kurt

Reprint: Zur Approximation algebraischer Zahlen. II: Über die Anzahl der Darstellungen ganzer Zahlen durch Binärformen (1933)

Doc. Math. Extra Vol. Mahler Selecta, 367-386 (2019)
DOI: 10.25537/dm.2019.SB-367-386


Extending his work in Part I, Mahler now shows that the number of representations of a rational integer \(g\) by a binary form \(F(x,y)\) is at most \(O(|g|^{\varepsilon})\), where \(\varepsilon\) is any arbitrarily small positive constant. \par Reprint of the author's paper [Math. Ann. 108, 37--55 (1933; Zbl 0006.15604; JFM 39.0269.01)]. For Part I see [Zbl 1465.11012].

Mathematics Subject Classification

11-03, 11J68