45 citations · 246 across the 34 of their papers we have counts for
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Secondary terms in the counting functions of quartic fields II
Arul Shankar, Jacob Tsimerman
We determine the smoothed counts of -quartic fields with bounded discriminant, satisfying any finite specified set of local conditions, as the sum of two main terms with a pow…
The second moment of the size of the -class group of monogenized cubic fields
Manjul Bhargava, Arul Shankar, Ashvin Swaminathan
We prove that when totally real (resp., complex) monogenized cubic number fields are ordered by height, the second moment of the size of the -class group is at most (resp.,…
Malle's Conjecture for Galois octic fields over
Arul Shankar, Ila Varma
We compute the asymptotic number of octic number fields whose Galois groups over are isomorphic to , the symmetries of a square, when ordering such fields by their…
Finiteness theorems for some representations of
Fatemehzahra Janbazi, Arul Shankar
Let be an integer and let be a number field with ring of integers . We prove that the set of ternary -ic forms with coefficients in …
Secondary terms in the counting functions of quartic fields
Arul Shankar, Jacob Tsimerman
We prove that the smoothed counting function of the set of quartic fields, satisfying any finite set of local conditions, can be written as a linear combination of $X,X^{5/6}\log X…