Arul Shankar, Ph.D.

Mathematics Harvard University, Cambridge, MA, United States 
 2013 Mathematics Princeton University, Princeton, NJ 
"Arul Shankar"


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Manjul Bhargava grad student 2013 Princeton
 (The average rank of elliptic curves over number fields.)
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Bhargava M, Shankar A. (2015) Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0 Annals of Mathematics. 181: 587-621
Bhargava M, Shankar A. (2015) Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves Annals of Mathematics. 181: 191-242
Bhargava M, Shankar A, Tsimerman J. (2013) On the Davenport-Heilbronn theorems and second order terms Inventiones Mathematicae. 193: 439-499
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