Ideal class groups of cyclotomic fields and modular forms of level 1
type: Item
instance of: scholarly article
title: Ideal class groups of cyclotomic fields and modular forms of level 1
zbMATH Open document ID: 0797.11087
author: Masato Kurihara
published in: Journal of Number Theory
publication date: 1994-01-13T00:00:00Z
review text: Let \(p\) be an odd prime, and let \(A\) denote the \(p\)-Sylow subgroup of the ideal class group of the cyclotomic field \(\mathbb{Q} (\mu_ p)\). The author studies the following conjecture, which would follow from Vandiver's Conjecture: For each odd character \(\psi\) of \(\text{Gal} (\mathbb{Q} (\mu_ p)/ \mathbb{Q})\), which is not the Teichmüller character, the \(\psi\)- eigenspace of \(A\) is cyclic of order \(L(0,\psi^{-1})\). This conjecture is related to the structure of the Hecke algebra of level 1 modular forms.
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11F11
zbMATH DE Number: 483989
zbMATH Keywords: \(L\)-functions
zbMATH Keywords: Eisenstein ideal
zbMATH Keywords: Vandiver's conjecture
zbMATH Keywords: Hecke algebra
reviewed by: Manfred Kolster
MaRDI profile type: Publication
full work available at URL: jnth.1993.1078
OpenAlex ID: W2001274830
DOI: 10.1006/JNTH.1993.1078
description: scientific article; zbMATH DE number 483989