most citedCommon divisors of a^n-1 and b^n-1 over function fields

11 citations · 11 across the 3 of their papers we have counts for

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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…