Analytic problems for elliptic curves

Abstract

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 (Note : This paper was initially written in 2000/01, but after a four year wait for a referee report, it is now withdrawn and deposited in the arXiv).

65 pages

Cited by in corpus (7)

• Amicable pairs and aliquot cycles for elliptic curves
• Averages of the number of points on elliptic curves
• On the average exponent of CM Elliptic Curves Modulo p
• The average of the first invariant factor for reductions of CM elliptic curves mod $p$
• Mean-Value of Product of Shifted Multiplicative Functions and Average Number of Points on Elliptic Curves
• Pseudoprime reductions of Elliptic curves
• Generating functions for power moments of elliptic curves over ${\mathbb{F}}_p$