Poisson distribution of a prime counting function corresponding to elliptic curves
| Autor: | Balasubramanian, R., Giri, Sumit |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Int Math Res Notices (2016) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1093/imrn/rnw035 |
| Popis: | 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. Comment: 17 pages |
| Databáze: | arXiv |
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