17 citations · 27 across the 5 of their papers we have counts for
Showing 2004Show all
3 papers · 1 filter
math.NT2004★ 1 cited
Root numbers and ranks in positive characteristic
B. Conrad, K. Conrad, H. Helfgott
For a global field K and an elliptic curve E_eta over K(T), Silverman's specialization theorem implies that rank(E_eta(K(T))) <= rank(E_t(K)) for all but finitely many t in P^1(K).…
math.NT2004★ 7 cited
The parity problem for reducible cubic forms
H. A. Helfgott
Let f in Z[x,y] be a reducible homoegeneous polynomial of degree 3. We show that f(x,y) has an even number of prime factors as often as an odd number of prime factors.
math.NT2004
Integral points on elliptic curves and 3-torsion in class groups
H. A. Helfgott, A. Venkatesh
We give new bounds for the number of integral points on elliptic curves. The method may be said to interpolate between approaches via diophantine techniques ([BP], [HBR]) and metho…