Ordered by max(|A|,|B|), elliptic curves have average rank at most 1.5, proved via a new semi-invariant counting argument for binary quartic forms.
Secondary terms in the first moment of $|{\rm Sel}_2(E)|$
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
citation-role summary
background 1
citation-polarity summary
fields
math.NT 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Boundedness of average rank of elliptic curves ordered by the coefficients
Ordered by max(|A|,|B|), elliptic curves have average rank at most 1.5, proved via a new semi-invariant counting argument for binary quartic forms.