On an effective order estimate of the Dirichlet \(L\)-functions in the critical strip
type: Item
instance of: scholarly article
title: On an effective order estimate of the Dirichlet \(L\)-functions in the critical strip
zbMATH Open document ID: 0824.11049
author: Mieczysław Kulas
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 1995-11-15T00:00:00Z
review text: Es sei \(\chi\) ein Dirichletscher Charakter \(\pmod k\). Der Verf. beweist für \({1\over 2}\leq \sigma\leq 1\), \(| t|\geq 2\) \[ | L(\sigma+ it, \chi)|\leq ck^{1-\sigma} | t|^{\alpha (1- \sigma)^{3/2}} \max (\log k, \log^{2/3} | t|) \] mit \(\alpha= 21,5028\) und einer numerischen Konstanten \(c\). Damit verschärft er eine analoge Abschätzung von \textit{E. I. Panteleeva} [Mat. Zametki 44, 494- 505 (1988; Zbl 0665.10028)]. Der Beweis beruht auf der Abschätzung \[ \Bigl| \sum_{kN< n\leq kN_ 1} \chi(n)\;n^{it} \Bigr|\leq AkN \exp \{-B \log^ 3 N/\log^ 2 t\} \] für \(N,N_ 1\in \mathbb{N}\), \(2\leq N\leq t/2\), \(N_ 1\leq 2N\), \(t\geq t_ 0\) mit einer numerischen Konstanten \(A\) und \(B= 1/3121\).
Mathematics Subject Classification ID: 11M06
zbMATH DE Number: 713624
zbMATH Keywords: effective order estimate
zbMATH Keywords: Dirichlet \(L\)-functions
zbMATH Keywords: critical strip
reviewed by: Wolfgang Haneke
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 713624