45 citations · 246 across the 34 of their papers we have counts for
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math.NT2010
Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0
Manjul Bhargava, Arul Shankar
We prove an asymptotic formula for the number of -equivalence classes of integral ternary cubic forms having bounded invariants. We use this result to show…
math.NT2010
Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves
Manjul Bhargava, Arul Shankar
We prove a theorem giving the asymptotic number of binary quartic forms having bounded invariants; this extends, to the quartic case, the classical results of Gauss and Davenport i…
math.NT2010★ 8 cited
On the Davenport-Heilbronn theorems and second order terms
Manjul Bhargava, Arul Shankar, Jacob Tsimerman
We give simple proofs of the Davenport--Heilbronn theorems, which provide the main terms in the asymptotics for the number of cubic fields having bounded discriminant and for the n…