Average Rank of Elliptic Curves Bounded by 7/6 via Selmer Group Sizes — E8 Intelligence Research

FINDING: Bhargava–Shankar proved the average rank of elliptic curves over ℚ is bounded (≤ 7/6), with average size of n-Selmer groups exactly n+1 for n=2,3,4,5. | MATH: lim_{X→∞} (1/N(X)) Σ_{E: ht(E) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-01
DOI
https://doi.org/10.5281/zenodo.22225596
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

Average Rank of Elliptic Curves Bounded by 7/6 via Selmer Group Sizes — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

Average Rank of Elliptic Curves Bounded by 7/6 via Selmer Group Sizes — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Bhargava–Shankar proved the average rank of elliptic curves over ℚ is bounded (≤ 7/6), with average size of n-Selmer groups exactly n+1 for n=2,3,4,5. | MATH: lim_{X→∞} (1/N(X)) Σ_{E: ht(E) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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