A Simple Proof of Siegel's Theorem Using Mellin Transform

2022/01/30 by Zihao Liu, Liu, Zihao
Computer Science · Mathematics · #11M20 #Analytic Number Theory Research #Analytic and geometric function theory #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2202.00635

openalex publication_date 2022/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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