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Arul Shankar

Harvard University

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Publication

Featured researches published by Arul Shankar.

Annals of Mathematics | 2015

Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves

Manjul Bhargava; Arul Shankar

Inventiones Mathematicae | 2013

On the Davenport–Heilbronn theorems and second order terms

Manjul Bhargava; Arul Shankar; Jacob Tsimerman

Annals of Mathematics | 2015

Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0

Manjul Bhargava; Arul Shankar

arXiv: Number Theory | 2013

The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1

Manjul Bhargava; Arul Shankar

arXiv: Number Theory | 2013

The average number of elements in the 4-Selmer groups of elliptic curves is 7

Manjul Bhargava; Arul Shankar

arXiv: Number Theory | 2014

COUNTING -FIELDS WITH A POWER SAVING ERROR TERM

Arul Shankar; Jacob Tsimerman

arXiv: Number Theory | 2016

Squarefree values of polynomial discriminants I

Manjul Bhargava; Arul Shankar; Xiaoheng Wang

arXiv: Number Theory | 2017

Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves

Manjul Bhargava; Arul Shankar; Takashi Taniguchi; Frank Thorne; Jacob Tsimerman; Yongqiang Zhao

arXiv: Number Theory | 2015

Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces

Manjul Bhargava; Arul Shankar; Xiaoheng Wang

arXiv: Number Theory | 2015

AVERAGE RANK OF ELLIPTIC CURVES

Séminaire Bourbaki; Arul Shankar; Bjorn Poonen

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Collaboration

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Manjul Bhargava

Princeton University

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Jacob Tsimerman

Princeton University

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Ila Varma

Princeton University

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Nicolas Templier

Princeton University

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Xiaoheng Wang

Princeton University

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Anders Södergren

University of Copenhagen

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Bjorn Poonen

Massachusetts Institute of Technology

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Frank Thorne

University of South Carolina

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Wei Ho

University of Michigan

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Takashi Taniguchi

University of Tokyo

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