On the asymptotic formula of L'(1, χ)

2013/10/10 by Luhao Yan, Yan, Luhao
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1310.2715

13 pages

arxiv created 2013/10/10 · openalex publication_date 2013/10/10 · arxiv updated 2013/10/11 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

Let χ be a quadratic Dirichlet character. In some literatures, various asymptotic formulae of L'(1,χ), under the assumption that L(1,χ) takes a small value, were derived. In this paper, we will give a new treatment unified for the odd and even cases, not depending on Kronecker limit formula. For imaginary quadratic fields, our result coincides with Proposition 22.10 in [1].

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