A bound for the least Gaussian prime \(\omega\) with \(\alpha<\arg(\omega)<\beta\)
type: Item
instance of: scholarly article
title: A bound for the least Gaussian prime \(\omega\) with \(\alpha<\arg(\omega)<\beta\)
zbMATH Open document ID: 1008.11043
author: Hajime Matsui
published in: Archiv der Mathematik
publication date: 2003-03-05T00:00:00Z
review text: Let \(\alpha, \beta\) be real numbers satisfying \(\alpha < \beta \leq \alpha + \frac{\pi}{2}\) . The author proves that there exists a Gaussian prime \(\omega\) with \(\alpha < \arg (\omega) < \beta\) such that \[ \omega \overline{\omega}< \exp \left( \frac{A}{\sqrt{\beta - \alpha}} \left( \log \frac{1}{\beta - \alpha} \right)^{3/2} \right), \] where \(A\) is a positive absolute constant. Under the assumption of the Generalized Riemann Hypothesis this estimate can be improved to \[ \omega \overline{\omega}< \frac{A}{(\beta - \alpha)^2} \log^4 \frac{1}{\beta - \alpha} . \]
Mathematics Subject Classification ID: 11R44
Mathematics Subject Classification ID: 11R11
zbMATH DE Number: 1508339
zbMATH Keywords: Gaussian prime
reviewed by: Jürgen Hinz
MaRDI profile type: Publication
full work available at URL: s000130050463
OpenAlex ID: W230746476
DOI: 10.1007/S000130050463
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description: scientific article; zbMATH DE number 1508339