On the minimal set for counterexamples to the local-global principle
  We prove that only for powers of 2 and 3 could occur counterexamples to the local-global divisibility principle for elliptic curves defined over the rationals. For we refine our previous criterion for the validity of the principle. We also give an example that shows that the assumptions of our criterion are necessary. 
Laura Paladino, Gabriele Ranieri, Evelina Viada
math.NT