Reprint: On the approximation to algebraic numbers. II: On the number of representations of integers by binary forms (1933)

Abstract

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.

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].