Arul Shankar

1. Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves
   2010/06/04 by Manjul Bhargava, Arul Shankar, Bhargava, Manjul +1 · 17 citations
   Mathematics · #11E76 #11G05 #11R45 #FOS: Mathematics #Number Theory (math.NT)
2. Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0
   2010/06/30 by Manjul Bhargava, Arul Shankar, Bhargava, Manjul +1 · 11 citations
   Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research
3. The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1
   2013/12/30 by Manjul Bhargava, Bhargava, Manjul, Arul Shankar +1 · 1 voice · 9 citations
   Computer Science · Mathematics · #11G05 #11R45 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)
4. On the Davenport-Heilbronn theorems and second order terms
   2010/05/05 by Manjul Bhargava, Arul Shankar, Bhargava, Manjul +3 · 10 citations
   Mathematics · #11R16 #11R45 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
5. Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves
   2017/01/10 by Manjul Bhargava, Arul Shankar, Bhargava, Manjul +9 · 9 citations
   Mathematics · Social Sciences · #11G05 #11R29 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #China's Ethnic Minorities and Relations #FOS: Mathematics #Number Theory (math.NT)
6. Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces
   2015/12/09 by Manjul Bhargava, Arul Shankar, Bhargava, Manjul +3 · 6 citations
   Mathematics · #Algebraic Geometry and Number Theory #advanced mathematical theories #Mathematical Dynamics and Fractals
7. Remarks on the disproof of the unit distance conjecture
   2026/05/20 by Noga Alon, Thomas F. Bloom, W. T. Gowers +6 · 4 voices · 11 citations
   #math.CO #math.NT
8. An improvement on Schmidt's bound on the number of number fields of bounded discriminant and small degree
   2022/04/04 by Manjul Bhargava, Bhargava, Manjul, Arul Shankar +3 · 3 citations
   Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)
9. The mean number of 2-torsion elements in the class groups of n-monogenized cubic fields
   2020/10/29 by Manjul Bhargava, Bhargava, Manjul, Jonathan Hanke +3 · 3 citations
   Mathematics · #11R16 #11R29 #11R45 #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)
10. Counting S₅-fields with a power saving error term
    2013/10/08 by Arul Shankar, Jacob Tsimerman, Shankar, Arul +1 · 1 citation
    Mathematics · #11R45 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
11. The number of quartic D₄-fields ordered by conductor
    2017/04/06 by Salim Ali Altuğ, Arul Shankar, Altug, Salim Ali +5 · 1 citation
    Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
12. Malle's Conjecture for Galois octic fields over \mathbb Q
    2025/05/29 by Arul Shankar, Ila Varma, Shankar, Arul +1 · 1 citation
    Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Commutative Algebra and Its Applications