Secondary terms in the first moment of $|{\mathrm{Sel}}_2(E)|$

Arul Shankar, Takashi Taniguchi

We prove the existence of secondary terms of order $X^{3/4}$, with power saving error terms, in the counting functions of $|{\mathrm{Sel}}_2(E)|$, the 2-Selmer group of E, for elliptic…