Metrical Theorems on Restricted Diophantine Approximations to Points on a Curve Original Research Article

We investigate rational approximations (r/p,q/p) or (r/p,q/r) to points on the curve (α,ατ) for almost all α>0, where p,q,r are all primes. We immediately obtain corollaries on making p,[αp], [ατp] simultaneously prime.