Chennai Mathematical Institute


3.30 p.m., Seminar Hall
Dr. P. Sheel Memorial Medal Lecture of the National Academy of Sciences, Allahabad
Elliptic curves and Poisson distribution

R. Balasubramanian
Institute of Mathematical Sciences, Chennai., Chennai.


Let $ E$ be an elliptic curve defined over rational field $Q$ and $N$ be a positive integer. Now $M_E(N)$ denotes the number of primes $p$, such that the group $E_p(F_p)$ is of order $N$. We show that $M_E(N)$ follows Poisson distribution when an average is taken over a large class of curves.