An adelic setting of some functions analogous to \(\log|\eta (z)|)\)
type: Item
instance of: scholarly article
title: An adelic setting of some functions analogous to \(\log|\eta (z)|)\)
zbMATH Open document ID: 0586.10017
DOI: 10.1016/0022-314X(86)90008-9
author: Yves Driencourt
published in: Journal of Number Theory
publication date: 1986-01-01T00:00:00Z
review text: Let \(F\) be a number field, \(\mathbb A\) the adeles of \(F\), and \(D\) an irreducible representation of the standard maximal compact subgroup of \(\mathrm{SL}(2,\mathbb A)\). The author studies the adelic Eisenstein series attached to \(D\) when (1) \(F=\mathbb Q\) and \(D_{\infty}=1\) or (2) \(F\) has class number one and \(D\) is trivial. In (1) he recovers the known Fourier expansion of classical Eisenstein series of arbitrary level. In (2) he recovers a generalization of Kronecker's first limit formula, due to \textit{T. Asai} [Nagoya Math. J. 40, 193--211 (1970; Zbl 0213.05701)].
reviewed by: Avner Ash
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11R56
zbMATH DE Number: 3939427
zbMATH Keywords: irreducible representation
zbMATH Keywords: maximal compact subgroup of SL(2, A)
zbMATH Keywords: adelic Eisenstein series
zbMATH Keywords: class number
MaRDI profile type: Publication
cites work: On a Certain Function Analogous to log|η(z)|
cites work: Q4090435
cites work: Fonctions de Whittaker associées aux groupes de Chevalley
cites work: Q5519244
cites work: Lectures on modular functions of one complex variable
cites work: Q4771024
cites work: On the Eisenstein Series for the Principal Congruence Subgroups
description: scientific article; zbMATH DE number 3939427