17 citations · 27 across the 5 of their papers we have counts for
7 papers
The parity problem for irreducible cubic forms
H. A. Helfgott
Let f\in \mathbb{Z}[x,y] be an irreducible homogeneous 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.
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).…
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.
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…
Root numbers and the parity problem
Harald Helfgott
Let E be a one-parameter family of elliptic curves over a number field. It is natural to expect the average root number of the curves in the family to be zero. All known counterexa…
Edge Effects on Local Statistics in Lattice Dimers: A Study of the Aztec Diamond (Finite Case)
Harald Helfgott
We compute the probability of any local pattern at an arbitrary position in a random dimer configuration in a square grid with an Aztec-diamond boundary.