2005/10/10 by Emmanuel Kowalski, Kowalski, Emmanuel
Computer Science · Mathematics · #11F99 #11G05 #11G20 #11N99 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F99 #msc:11G05 #msc:11G20 #msc:11N99
paper · pdf · doi:10.48550/arxiv.math/0510197
65 pages
arxiv created 2005/10/10 · openalex publication_date 2005/10/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider some problems of analytic number theory for elliptic curves which can be considered as analogues of classical questions around the distribution of primes in arithmetic progressions to large moduli, and of the question of twin primes. This leads to some local results on the distribution of the group structures of elliptic curves defined over a prime finite field, exhibiting an interesting dichotomy for the occurence of the possible groups. (Note : This paper was initially written in 2000/01, but after a four year wait for a referee report, it is now withdrawn and deposited in the arXiv).