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

  • Kurt Mahler


Extending his work in Part I, Mahler now shows that the number of representations of a rational integer gg by a binary form F(x,y)F(x,y) is at most O(gε)O(|g|^{\varepsilon}), where ε\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].