Note On Elliptic Groups of Prime Orders

N. A. Carella

Note On Elliptic Groups of Prime Orders

General Mathematics 2019-03-06 v4

Authors: N. A. Carella

Abstract

Let $E$ be an elliptic curve of rank $\text{rk}(E) \geq 1$ , and let $E(\mathbb{F}_p)$ be the elliptic group of order $\#E(\mathbb{F}_p)=n$ . The number of primes $p\leq x$ such that $n$ is prime is expected to be $\pi(x,E)=\delta(E)x/\log^2 x+o(x/\log^2 x)$ , where $\delta(E)\geq 0$ is the density constant. This note proves a lower bound $\pi(x,E) \gg x/\log^2 x$ .

Keywords

elliptic curves finite groups prime number theory

Cite

@article{arxiv.1702.06814,
  title  = {Note On Elliptic Groups of Prime Orders},
  author = {N. A. Carella},
  journal= {arXiv preprint arXiv:1702.06814},
  year   = {2019}
}

Comments

Twenty One Pages. Keywords: Elliptic Prime; Group of Prime Order, Primitive Point; Koblitz Conjecture. arXiv admin note: text overlap with arXiv:1703.06806

Note On Elliptic Groups of Prime Orders

Abstract

Keywords

Cite

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