Minkowski's theorem on nonhomogeneous approximation

Proof-critical source

Diophantine approximation on abelian varieties; a conjecture of M. Waldschmidt

This paper is included only for the following marked statement:

• Nonhomogeneous $1/4$ theorem · Proc. AMS 12 (1961), 992–993For irrational $\alpha$ and $x\notin\mathbb Z\alpha+\mathbb Z$, infinitely many $q$ satisfy $q\lVert q\alpha-x\rVert<1/4$.