On the distribution of analytic ranks of elliptic curves

Peter J. Cho; Keunyoung Jeong

On the distribution of analytic ranks of elliptic curves

Number Theory 2020-04-13 v2

Authors: Peter J. Cho , Keunyoung Jeong

Abstract

In this paper, under GRH for elliptic $L$ -functions, we give an upper bound for the probability for an elliptic curve with analytic rank $\leq a$ for $a \geq 11$ , and also give an upper bound of $n$ -th moments of analytic ranks of elliptic curves. These are applications of counting elliptic curves with local conditions, for example, having good reduction at $p$ .

Keywords

elliptic curves analytic rank GRH probability upper bound moments local conditions

Cite

@article{arxiv.2003.09102,
  title  = {On the distribution of analytic ranks of elliptic curves},
  author = {Peter J. Cho and Keunyoung Jeong},
  journal= {arXiv preprint arXiv:2003.09102},
  year   = {2020}
}

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We change the organization

On the distribution of analytic ranks of elliptic curves

Abstract

Keywords

Cite

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