Arul Shankar
I am an assistant professor in Mathematics at
the University of
Toronto. My research is in Number Theory, specifically, in
Arithmetic Statistics and surrounding areas. You can contact me at
"arul dot shnkr at gmail dot com".
Papers and Preprints

Odd degree number fields with odd class number

with W. Ho
and I. Varma,
posted to the arxiv.

Lowlying zeros of certain families of Artin Lfunctions

with A. Södergren
and N. Templier,
posted to the arxiv.

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

with M. Bhargava, submitted.

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

with M. Bhargava, submitted.

Counting S_{5} fields with a power saving error term

with J. Tsimerman,
published in the Forum of Mathematics, Sigma.

Average size of the 2Selmer group of Jacobians of monic
even hyperelliptic curves

with X. Wang, posted to the arxiv.

Abelian surfaces over finite fields with prescribed groups

with C David,
D. Garton, Z. Scherr,
E. Smith, L. Thompson,
published in the Bulletin of the London Mathematical Society.

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

with M. Bhargava, published in the Annals of Mathematics.

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

with M. Bhargava, published in the Annals of Mathematics.

On the DavenportHeilbronn theorems and second order terms

with M. Bhargava and J. Tsimerman, published in Inventiones Mathematicae.
Current courses
 Math 223b: Algebraic Number Theory, Spring 2016