A Simple Proof of Siegel's Theorem Using Mellin Transform

Zihao Liu

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arXiv · 2202.00635

A Simple Proof of Siegel's Theorem Using Mellin Transform

Zihao Liu

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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 $\Gamma(s)$.

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Zihao Liu. 2022-01-30. A Simple Proof of Siegel's Theorem Using Mellin Transform. https://arxiv.org/abs/2202.00635

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