Lower bound for the 2-adic valuations of central $L$-values of elliptic curves with complex multiplication

Keiichiro Nomoto

Lower bound for the 2-adic valuations of central $L$-values of elliptic curves with complex multiplication

Number Theory 2023-01-11 v2

Authors: Keiichiro Nomoto

Abstract

Let $E_{-D}$ be the elliptic curve $y^2=x^3+Dx$ defined over $K=\mathbb{Q}(i)$ for $D\in K$ which is coprime to 2. In this paper, we give a lower bound for the 2-adic valuation of the algebraic part of the central value of Hecke $L$ -function associated to $E_{-D}$ .

Keywords

elliptic curves complex multiplication 2-adic valuation central l-value hecke l-function

Cite

@article{arxiv.2207.10380,
  title  = {Lower bound for the 2-adic valuations of central $L$-values of elliptic curves with complex multiplication},
  author = {Keiichiro Nomoto},
  journal= {arXiv preprint arXiv:2207.10380},
  year   = {2023}
}

Comments

20 pages

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