Poisson distribution of a prime counting function corresponding to elliptic curves

R. Balasubramanian; Sumit Giri

doi:10.1093/imrn/rnw035

Poisson distribution of a prime counting function corresponding to elliptic curves

R. Balasubramanian, Sumit Giri^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	7369-7389
Number of pages	21
Journal	International Mathematics Research Notices
Volume	2016
Issue number	24
DOIs	https://doi.org/10.1093/imrn/rnw035
State	Published - Dec 2016
Externally published	Yes

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

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Poisson distribution of a prime counting function corresponding to elliptic curves

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