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arXiv · 1503.01018

Poisson distribution of a prime counting function corresponding to elliptic curves

R. Balasubramanian·Sumit Giri
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Abstract

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

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R. Balasubramanian, Sumit Giri. 2015-03-03. Poisson distribution of a prime counting function corresponding to elliptic curves. https://doi.org/10.1093/imrn%2Frnw035

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