30 citations · 34 across the 2 of their papers we have counts for
4 papers
The even parity Goldfeld conjecture: congruent number elliptic curves
Ashay Burungale, Ye Tian
In 1979 Goldfeld conjectured: 50\% of the quadratic twists of an elliptic curve defined over the rationals have analytic rank zero. In this expository article we present a few rece…
Indivisibility of Heegner points and arithmetic applications
Ashay Burungale, Francesc Castella, Chan-Ho Kim
We upgrade Howard's divisibility towards Perrin-Riou's Heegner point main conjecture to the predicted equality. Contrary to previous works in this direction, our main result allows…
Horizontal variation of Tate--Shafarevich groups
Ashay A. Burungale, Haruzo Hida, Ye Tian
Let be an elliptic curve over . Let be an odd prime and an embedding. Let be an imaginary quadratic f…
On the non-triviality of the -adic Abel-Jacobi image of generalised Heegner cycles modulo , II: Shimura curves
Ashay A. Burungale
Generalised Heegner cycles are associated to a pair of an elliptic newform and a Hecke character over an imaginary quadratic extension $K/\Q$. The cycles live in a middle dimension…