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On Bhargava’s representations and Vinberg’s invariant theory
, 2011
"... Manjul Bhargava has recently made a great advance in the arithmetic theory of elliptic curves. Together with his student, Arul Shankar, he determines the average order of the Selmer group Sel(E,m) for an elliptic curve E over Q, when m = 2, 3, 4, 5. We recall that the Selmer group is a finite subgro ..."
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Cited by 6 (5 self)
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Manjul Bhargava has recently made a great advance in the arithmetic theory of elliptic curves. Together with his student, Arul Shankar, he determines the average order of the Selmer group Sel(E,m) for an elliptic curve E over Q, when m = 2, 3, 4, 5. We recall that the Selmer group is a finite
The average rank of elliptic curves over number fields
, 2013
"... In joint work with Manjul Bhargava (see [7]), we proved that the average rank of rational elliptic curves, when ordered by their heights, is bounded above by 1.5. This result was accomplished by using Bhargava’s geometryofnumbers methods (developed in [1] and [2]) to obtain asymptotics for the nu ..."
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In joint work with Manjul Bhargava (see [7]), we proved that the average rank of rational elliptic curves, when ordered by their heights, is bounded above by 1.5. This result was accomplished by using Bhargava’s geometryofnumbers methods (developed in [1] and [2]) to obtain asymptotics
Hanoi lectures on the arithmetic of hyperelliptic curves
, 2012
"... Manjul Bhargava and I have recently proved a result on the average order of the 2Selmer groups of the Jacobians of hyperelliptic curves of a fixed genus n ≥ 1 over Q, with a rational Weierstrass point [2, Thm 1]. A surprising fact which emerges is that the average order of this finite group is equa ..."
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Cited by 2 (1 self)
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Manjul Bhargava and I have recently proved a result on the average order of the 2Selmer groups of the Jacobians of hyperelliptic curves of a fixed genus n ≥ 1 over Q, with a rational Weierstrass point [2, Thm 1]. A surprising fact which emerges is that the average order of this finite group
forced to write calculus equations in center ring. Ideal Multiplication in Fields of Low Degree A Preliminary Report
"... with issues that arise in congenially detailing an algorithm for multiplication of ideals in quadratic fields. I briefly illustrate Bhargava’s work by giving my take on its application to the well known quadratic case, hoping thereby to instance and hint at its generalisations to cubic, and quartic ..."
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fields. Manjul Bhargava’s work on higher composition laws amply deals with issues that arise in congenially detailing an algorithm for multiplication of ideals in quadratic fields. I briefly illustrate Bhargava’s work by giving my take on its application to the well known quadratic case, hoping thereby
Contemporary Mathematics Universal Quadratic Forms and the Fifteen Theorem
"... Abstract. This paper is an extended foreword to the paper of Manjul Bhargava [1] in these proceedings, which gives a short and elegant proof of the ConwaySchneeberger Fifteen Theorem on the representation of integers by quadratic forms. The representation theory of quadratic forms has a long histor ..."
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Abstract. This paper is an extended foreword to the paper of Manjul Bhargava [1] in these proceedings, which gives a short and elegant proof of the ConwaySchneeberger Fifteen Theorem on the representation of integers by quadratic forms. The representation theory of quadratic forms has a long
Aisenstadt Chairs Le Bulletin du CRM Analysis in Number Theory
"... will consist of two semesters with different foci, both exploring the fruitful interactions between analysis and number theory. In many areas of number theory, one is led to the study and understanding of analytic objects, such as the ubiquitous Lfunctions, which appear in various forms in differen ..."
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of the leading researchers in their fi elds. The 20052006 AndréAisenstadt chairs are Manjul Bhargava (Princeton), K. Soundararajan (Michigan) and Terry Tao (UCLA), who will be visiting the CRM for two months, six months and two weeks respectively. Some of the activities of the theme year are organised jointly