Zeta-functions of binary Hermitian forms
type: Item
instance of: scholarly article
title: Zeta-functions of binary Hermitian forms
zbMATH Open document ID: 0834.11018
DOI: 10.1007/BF00975116
published in: Lithuanian Mathematical Journal
publication date: 1995-09-11T00:00:00Z
review text: Motivated by the work of \textit{J. Elstrodt}, \textit{F. Grunewald} and \textit{J. Mennicke} on zeta-functions of binary Hermitian forms [Math. Ann. 277, 655--708 (1987; Zbl 0659.10021)] the author investigates zeta-functions of binary Hermitian forms over the ring of integers of the extension \(\mathbb{Q} (i, \sqrt {2})\) over \(\mathbb{Q} (\sqrt {2})\). For any integer \(\Delta\) of \(\mathbb{Q} (\sqrt {2})\) an associated zeta-function \(Z (\Delta, s)\) is defined. This zeta-function has an Euler product expansion. The main result of the work under review is an explicit determination of the coefficients of the Euler factors of \(Z (\Delta, s)\). This yields an explicit formula for the Euler product of \(Z (\Delta, s)\).
Mathematics Subject Classification ID: 11E45
Mathematics Subject Classification ID: 11E39
zbMATH DE Number: 794481
zbMATH Keywords: zeta-functions
zbMATH Keywords: binary Hermitian forms
zbMATH Keywords: Euler product
zbMATH Keywords: explicit formula
author: Edmundas Gaigalas
reviewed by: Jürgen Elstrodt
MaRDI profile type: Publication
cites work: Zeta-functions of binary Hermitian forms and special values of Eisenstein series
full work available at URL: https://doi.org/10.1007/bf00975116
OpenAlex ID: W2066606718
description: scientific article; zbMATH DE number 794481