A Simple Proof of Siegel's Theorem Using Mellin Transform

Zihao Liu

A Simple Proof of Siegel's Theorem Using Mellin Transform

Number Theory 2022-02-02 v1

Authors: Zihao Liu

Abstract

In this paper, we present a simple analytic proof of Siegel's theorem that concerns the lower bound of $L(1,\chi)$ for primitive quadratic $\chi$ . Our new method compares an elementary lower bound with an analytic upper bound obtained by the inverse Mellin transform of $\Gamma(s)$ .

Keywords

fundamental theorem bound upper bounds

Cite

@article{arxiv.2202.00635,
  title  = {A Simple Proof of Siegel's Theorem Using Mellin Transform},
  author = {Zihao Liu},
  journal= {arXiv preprint arXiv:2202.00635},
  year   = {2022}
}

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