39 citations · 205 across the 16 of their papers we have counts for
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A majority of elliptic curves over satisfy the Birch and Swinnerton-Dyer conjecture
Manjul Bhargava, Christopher Skinner, Wei Zhang
We prove that a majority (in fact, ) of all elliptic curves over , when ordered by height, satisfy the Birch and Swinnerton-Dyer rank conjecture.
Indivisibility of Heegner points in the multiplicative case
Christopher Skinner, Wei Zhang
For certain elliptic curves over with multiplicative reduction at a prime , we prove the -indivisibility of the derived Heegner classes defined with re…
Multiplicative reduction and the cyclotomic main conjecture for
Christopher Skinner
We show that the cyclotomic Iwasawa--Greenberg Main Conjecture holds for a large class of modular forms with multiplicative reduction at , extending previous results for the goo…
A converse to a theorem of Gross, Zagier, and Kolyvagin
Christopher Skinner
Let be a semistable elliptic curve over . We prove that if has non-split multiplicative reduction at at least one odd prime or split multiplicative reduction at…
A positive proportion of elliptic curves over have rank one
Manjul Bhargava, Christopher Skinner
We prove that, when all elliptic curves over are ordered by naive height, a positive proportion have both algebraic and analytic rank one. It follows that the average…