The average rank of elliptic curves I

1992/12/01 by Armand Brumer · 1 voice · 10 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic

paper · doi:10.1007/bf01232033

crossref issued 1992/12/01 · crossref published 1992/12/01 · crossref published-print 1992/12/01 · openalex publication_date 1992/12/01 · crossref created 2005/02/25 · crossref deposited 2020/04/06 · openalex created_date 2025/10/10 · crossref indexed 2026/06/02 · openalex updated_date 2026/07/23

Cited by

• On balanced subgroups of the multiplicative group
• The average number of elements in the 4-Selmer groups of elliptic curves is 7
• Low-lying zeros of families of elliptic curves
• The Average Analytic Rank of Elliptic Curves
• One- and two-level densities for rational families of elliptic curves: evidence for the underlying group symmetries
• On the low-lying zeros of Hasse–Weil L-functions for elliptic curves
• ON THE NON-VANISHING OF ELLIPTIC CURVE L-FUNCTIONS AT THE CENTRAL POINT
• Databases of elliptic curves ordered by height and distributions of Selmer groups and ranks
• ONE-LEVEL DENSITY OF LOW-LYING ZEROS OF QUADRATIC HECKE L-FUNCTIONS OF IMAGINARY QUADRATIC NUMBER FIELDS
• Rank of an elliptic curve [wikipedia]

Discussions

• The Katz-Sarnak conjecture, which I phrase roughly as follows because I don't believe it has ever been formulated in a precise manner with respect to exactly which height functions should work, is rou [stackexchange, 8 points]