11 citations · 11 across the 3 of their papers we have counts for
3 papers
math.NT2004★ 11 cited
Common divisors of a^n-1 and b^n-1 over function fields
Joseph H. Silverman
Ailon and Rudnick have shown that if are multiplicatively independent polynomials, then is bounded for all . We show that if instead $a…
math.NT2003
A Lower Bound for the Canonical Height on Abelian Varieties over Abelian Extensions
Matthew Baker, Joseph Silverman
Let A be an abelian variety defined over a number field K, and consider the canonical height function attached to a symmetric ample line bundle L on A. We prove that there is a pos…
math.NT2003
A lower bound for the canonical height on elliptic curves over abelian extensions
Joseph H. Silverman
Let E/K be an ellptic curve defined over a number field, let h be the canonical height on E, and let K^ab be the maximal abelian extension of K. Extending work of M. Baker, we prov…