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arXiv · 2412.00995

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

Arul Shankar·Takashi Taniguchi
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Abstract

We prove the existence of secondary terms of order $X^{3/4}$, with power saving error terms, in the counting functions of $|{\rm Sel}_2(E)|$, the 2-Selmer group of E, for elliptic curves E having height bounded by X. This is the first improvement on the error term of $o(X^{5/6})$, proved by Bhargava--Shankar, where the primary term of order $X^{5/6}$ for this counting function was obtained.

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Arul Shankar, Takashi Taniguchi. 2024-12-01. Secondary terms in the first moment of $|{\rm Sel}_2(E)|$. https://arxiv.org/abs/2412.00995

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