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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…
Secondary terms in the first moment of
Arul Shankar, Takashi Taniguchi
We prove the existence of secondary terms of order , with power saving error terms, in the counting functions of , the 2-Selmer group of E, for elliptic…
Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves
Manjul Bhargava, Arul Shankar, Takashi Taniguchi +3
We prove the first known nontrivial bounds on the sizes of the 2-torsion subgroups of the class groups of cubic and higher degree number fields (the trivial bound being $O_ε(|{…