Eisenstein series in hyperbolic 3-space and Kronecker limit formula for biquadratic field

Let L = K be the composite of two imaginary quadratic fields and K. Suppose that the discriminants of and K are relatively prime. For any primitive ray class character χ of L, we shall compute L(1, χ) for the Hecke L-function in L. We write for the conductor of χ and C for the ray class modulo . Let...

Full description

Saved in:
Bibliographic Details
Published in:Nagoya mathematical journal 1989-03, Vol.113, p.129-146
Main Author: Konno, Shuji
Format: Article
Language:English
Subjects:
11F30
11R42
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c389t-896ffb4f464947f2c499de0320d38710629a2f835045e27e022fbea6386730d13
cites cdi_FETCH-LOGICAL-c389t-896ffb4f464947f2c499de0320d38710629a2f835045e27e022fbea6386730d13
container_end_page 146
container_issue
container_start_page 129
container_title Nagoya mathematical journal
container_volume 113
creator Konno, Shuji
description Let L = K be the composite of two imaginary quadratic fields and K. Suppose that the discriminants of and K are relatively prime. For any primitive ray class character χ of L, we shall compute L(1, χ) for the Hecke L-function in L. We write for the conductor of χ and C for the ray class modulo . Let c ε C be any integral ideal prime to . We write as g-module where g, n and ϑL are, respectively, the ring of integers in k, an ideal in k and the differente of L. Let where T(χ) is the Gaussian sum and, as in (3.2),
doi_str_mv 10.1017/S002776300000129X
format article
fullrecord <record><control><sourceid>cambridge_proje</sourceid><recordid>TN_cdi_projecteuclid_primary_oai_CULeuclid_euclid_nmj_1118781190</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1017_S002776300000129X</cupid><sourcerecordid>10_1017_S002776300000129X</sourcerecordid><originalsourceid>FETCH-LOGICAL-c389t-896ffb4f464947f2c499de0320d38710629a2f835045e27e022fbea6386730d13</originalsourceid><addsrcrecordid>eNp9kMtOwzAQRS0EEqXwAez8AwE_0tjegaryEJVYQCVYRY49Boe8sJNF_55EjdggMZs7mjvnSjMIXVJyRQkV1y-EMCEyTqaiTL0doQWjK5ZkMmXHaDHZyeSforMYy3FJcsUX6H3jIzSxB9_gCMFDxGP3ue8gFG3lDeZJ7LQBrBuLn0LbgPmCgCtf-x67NtRDpSfFhf8etA26HxnnobLn6MTpKsLFrEu0u9u8rh-S7fP94_p2mxguVZ9IlTlXpC7NUpUKx0yqlAXCGbFcCkoypjRzkq9IugImgDDmCtAZl5ngxFK-RDeH3C60JZgeBlN5m3fB1zrs81b7fL3bztNZmrrMKaVSSEoVGSPoIcKENsYA7pemJJ_em_9578jwmdF1Ebz9gLxsh9CMp_5D_QBIJ30X</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Eisenstein series in hyperbolic 3-space and Kronecker limit formula for biquadratic field</title><source>Project Euclid Complete</source><creator>Konno, Shuji</creator><creatorcontrib>Konno, Shuji</creatorcontrib><description>Let L = K be the composite of two imaginary quadratic fields and K. Suppose that the discriminants of and K are relatively prime. For any primitive ray class character χ of L, we shall compute L(1, χ) for the Hecke L-function in L. We write for the conductor of χ and C for the ray class modulo . Let c ε C be any integral ideal prime to . We write as g-module where g, n and ϑL are, respectively, the ring of integers in k, an ideal in k and the differente of L. Let where T(χ) is the Gaussian sum and, as in (3.2),</description><identifier>ISSN: 0027-7630</identifier><identifier>EISSN: 2152-6842</identifier><identifier>DOI: 10.1017/S002776300000129X</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>11F30 ; 11R42</subject><ispartof>Nagoya mathematical journal, 1989-03, Vol.113, p.129-146</ispartof><rights>Copyright © Editorial Board of Nagoya Mathematical Journal 1989</rights><rights>Copyright 1989 Editorial Board, Nagoya Mathematical Journal</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c389t-896ffb4f464947f2c499de0320d38710629a2f835045e27e022fbea6386730d13</citedby><cites>FETCH-LOGICAL-c389t-896ffb4f464947f2c499de0320d38710629a2f835045e27e022fbea6386730d13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,926,27924,27925</link.rule.ids></links><search><creatorcontrib>Konno, Shuji</creatorcontrib><title>Eisenstein series in hyperbolic 3-space and Kronecker limit formula for biquadratic field</title><title>Nagoya mathematical journal</title><addtitle>Nagoya Mathematical Journal</addtitle><description>Let L = K be the composite of two imaginary quadratic fields and K. Suppose that the discriminants of and K are relatively prime. For any primitive ray class character χ of L, we shall compute L(1, χ) for the Hecke L-function in L. We write for the conductor of χ and C for the ray class modulo . Let c ε C be any integral ideal prime to . We write as g-module where g, n and ϑL are, respectively, the ring of integers in k, an ideal in k and the differente of L. Let where T(χ) is the Gaussian sum and, as in (3.2),</description><subject>11F30</subject><subject>11R42</subject><issn>0027-7630</issn><issn>2152-6842</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1989</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EEqXwAez8AwE_0tjegaryEJVYQCVYRY49Boe8sJNF_55EjdggMZs7mjvnSjMIXVJyRQkV1y-EMCEyTqaiTL0doQWjK5ZkMmXHaDHZyeSforMYy3FJcsUX6H3jIzSxB9_gCMFDxGP3ue8gFG3lDeZJ7LQBrBuLn0LbgPmCgCtf-x67NtRDpSfFhf8etA26HxnnobLn6MTpKsLFrEu0u9u8rh-S7fP94_p2mxguVZ9IlTlXpC7NUpUKx0yqlAXCGbFcCkoypjRzkq9IugImgDDmCtAZl5ngxFK-RDeH3C60JZgeBlN5m3fB1zrs81b7fL3bztNZmrrMKaVSSEoVGSPoIcKENsYA7pemJJ_em_9578jwmdF1Ebz9gLxsh9CMp_5D_QBIJ30X</recordid><startdate>19890301</startdate><enddate>19890301</enddate><creator>Konno, Shuji</creator><general>Cambridge University Press</general><general>Duke University Press</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19890301</creationdate><title>Eisenstein series in hyperbolic 3-space and Kronecker limit formula for biquadratic field</title><author>Konno, Shuji</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c389t-896ffb4f464947f2c499de0320d38710629a2f835045e27e022fbea6386730d13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1989</creationdate><topic>11F30</topic><topic>11R42</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Konno, Shuji</creatorcontrib><collection>CrossRef</collection><jtitle>Nagoya mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Konno, Shuji</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Eisenstein series in hyperbolic 3-space and Kronecker limit formula for biquadratic field</atitle><jtitle>Nagoya mathematical journal</jtitle><addtitle>Nagoya Mathematical Journal</addtitle><date>1989-03-01</date><risdate>1989</risdate><volume>113</volume><spage>129</spage><epage>146</epage><pages>129-146</pages><issn>0027-7630</issn><eissn>2152-6842</eissn><abstract>Let L = K be the composite of two imaginary quadratic fields and K. Suppose that the discriminants of and K are relatively prime. For any primitive ray class character χ of L, we shall compute L(1, χ) for the Hecke L-function in L. We write for the conductor of χ and C for the ray class modulo . Let c ε C be any integral ideal prime to . We write as g-module where g, n and ϑL are, respectively, the ring of integers in k, an ideal in k and the differente of L. Let where T(χ) is the Gaussian sum and, as in (3.2),</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S002776300000129X</doi><tpages>18</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0027-7630
ispartof Nagoya mathematical journal, 1989-03, Vol.113, p.129-146
issn 0027-7630
2152-6842
language eng
recordid cdi_projecteuclid_primary_oai_CULeuclid_euclid_nmj_1118781190
source Project Euclid Complete
subjects 11F30
11R42
title Eisenstein series in hyperbolic 3-space and Kronecker limit formula for biquadratic field
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T16%3A19%3A20IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-cambridge_proje&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Eisenstein%20series%20in%20hyperbolic%203-space%20and%20Kronecker%20limit%20formula%20for%20biquadratic%20field&rft.jtitle=Nagoya%20mathematical%20journal&rft.au=Konno,%20Shuji&rft.date=1989-03-01&rft.volume=113&rft.spage=129&rft.epage=146&rft.pages=129-146&rft.issn=0027-7630&rft.eissn=2152-6842&rft_id=info:doi/10.1017/S002776300000129X&rft_dat=%3Ccambridge_proje%3E10_1017_S002776300000129X%3C/cambridge_proje%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c389t-896ffb4f464947f2c499de0320d38710629a2f835045e27e022fbea6386730d13%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_cupid=10_1017_S002776300000129X&rfr_iscdi=true