An explicit upper bound for Siegel zeros of imaginary quadratic fields

Dimbinaina Ralaivaosaona; Faratiana Brice Razakarinoro

An explicit upper bound for Siegel zeros of imaginary quadratic fields

Number Theory 2020-01-22 v2

Authors: Dimbinaina Ralaivaosaona , Faratiana Brice Razakarinoro

Abstract

For any integer $d\geq 3$ such that $-d$ is a fundamental discriminant, we show that the Dirichlet $L$ -function associated with the real primitive character $\chi(\cdot)=(\frac{-d}{\cdot})$ does not vanish on the positive part of the interval $[1-6.5/\sqrt{d},\ 1].$

Keywords

siegel zeros imaginary quadratic fields dirichlet l-function fundamental discriminant explicit bound

Cite

@article{arxiv.2001.05782,
  title  = {An explicit upper bound for Siegel zeros of imaginary quadratic fields},
  author = {Dimbinaina Ralaivaosaona and Faratiana Brice Razakarinoro},
  journal= {arXiv preprint arXiv:2001.05782},
  year   = {2020}
}

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18 pages, 2 figures

An explicit upper bound for Siegel zeros of imaginary quadratic fields

Abstract

Keywords

Cite

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