NEW BOUNDS FOR FUNDAMENTAL UNITS AND CLASS NUMBERS OF REAL QUADRATIC FIELDS

NEW BOUNDS FOR FUNDAMENTAL UNITS AND CLASS NUMBERS OF REAL QUADRATIC FIELDS

In this paper, we present new bounds on the fundamental units of real quadratic fields ${\mathbb{Q}}({\sqrt{d}})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide c...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Taehan Suhakhoe hoebo 2021, Vol.58 (5), p.1149-1161
Hauptverfasser: Isikay, Sevcan, Pekin, Ayten
Format: Artikel
Sprache:kor
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 1161
container_issue 5
container_start_page 1149
container_title Taehan Suhakhoe hoebo
container_volume 58
creator Isikay, Sevcan
Pekin, Ayten
description In this paper, we present new bounds on the fundamental units of real quadratic fields ${\mathbb{Q}}({\sqrt{d}})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.
format Article
fullrecord <record><control><sourceid>kisti</sourceid><recordid>TN_cdi_kisti_ndsl_JAKO202128557369139</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>JAKO202128557369139</sourcerecordid><originalsourceid>FETCH-kisti_ndsl_JAKO2021285573691393</originalsourceid><addsrcrecordid>eNqNir0OgjAYADtoIv68w7c4khRKEcZC24hAG_sTR2KiJihxqe8fGXwAp7vkboGiBCc0LnKSrdA6hCfGGU3LPEKtEheotFfcgtQG5GysF8qxDrxqnAWmONQdsxaU7ythLGgJRsz97Bk3zDU1yEZ03G7R8nGdwn334wbtpXD1MX6N4TMO71uYhhNrdYrTJC0oPZC8TEhJ_v2-Ef4y4w</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>NEW BOUNDS FOR FUNDAMENTAL UNITS AND CLASS NUMBERS OF REAL QUADRATIC FIELDS</title><source>EZB-FREE-00999 freely available EZB journals</source><creator>Isikay, Sevcan ; Pekin, Ayten</creator><creatorcontrib>Isikay, Sevcan ; Pekin, Ayten</creatorcontrib><description>In this paper, we present new bounds on the fundamental units of real quadratic fields ${\mathbb{Q}}({\sqrt{d}})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.</description><identifier>ISSN: 1015-8634</identifier><language>kor</language><ispartof>Taehan Suhakhoe hoebo, 2021, Vol.58 (5), p.1149-1161</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,4024</link.rule.ids></links><search><creatorcontrib>Isikay, Sevcan</creatorcontrib><creatorcontrib>Pekin, Ayten</creatorcontrib><title>NEW BOUNDS FOR FUNDAMENTAL UNITS AND CLASS NUMBERS OF REAL QUADRATIC FIELDS</title><title>Taehan Suhakhoe hoebo</title><addtitle>대한수학회보</addtitle><description>In this paper, we present new bounds on the fundamental units of real quadratic fields ${\mathbb{Q}}({\sqrt{d}})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.</description><issn>1015-8634</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>JDI</sourceid><recordid>eNqNir0OgjAYADtoIv68w7c4khRKEcZC24hAG_sTR2KiJihxqe8fGXwAp7vkboGiBCc0LnKSrdA6hCfGGU3LPEKtEheotFfcgtQG5GysF8qxDrxqnAWmONQdsxaU7ythLGgJRsz97Bk3zDU1yEZ03G7R8nGdwn334wbtpXD1MX6N4TMO71uYhhNrdYrTJC0oPZC8TEhJ_v2-Ef4y4w</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Isikay, Sevcan</creator><creator>Pekin, Ayten</creator><scope>JDI</scope></search><sort><creationdate>2021</creationdate><title>NEW BOUNDS FOR FUNDAMENTAL UNITS AND CLASS NUMBERS OF REAL QUADRATIC FIELDS</title><author>Isikay, Sevcan ; Pekin, Ayten</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-kisti_ndsl_JAKO2021285573691393</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>kor</language><creationdate>2021</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Isikay, Sevcan</creatorcontrib><creatorcontrib>Pekin, Ayten</creatorcontrib><collection>KoreaScience</collection><jtitle>Taehan Suhakhoe hoebo</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Isikay, Sevcan</au><au>Pekin, Ayten</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>NEW BOUNDS FOR FUNDAMENTAL UNITS AND CLASS NUMBERS OF REAL QUADRATIC FIELDS</atitle><jtitle>Taehan Suhakhoe hoebo</jtitle><addtitle>대한수학회보</addtitle><date>2021</date><risdate>2021</risdate><volume>58</volume><issue>5</issue><spage>1149</spage><epage>1161</epage><pages>1149-1161</pages><issn>1015-8634</issn><abstract>In this paper, we present new bounds on the fundamental units of real quadratic fields ${\mathbb{Q}}({\sqrt{d}})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.</abstract><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1015-8634
ispartof Taehan Suhakhoe hoebo, 2021, Vol.58 (5), p.1149-1161
issn 1015-8634
language kor
recordid cdi_kisti_ndsl_JAKO202128557369139
source EZB-FREE-00999 freely available EZB journals
title NEW BOUNDS FOR FUNDAMENTAL UNITS AND CLASS NUMBERS OF REAL QUADRATIC FIELDS
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-22T08%3A22%3A21IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-kisti&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=NEW%20BOUNDS%20FOR%20FUNDAMENTAL%20UNITS%20AND%20CLASS%20NUMBERS%20OF%20REAL%20QUADRATIC%20FIELDS&rft.jtitle=Taehan%20Suhakhoe%20hoebo&rft.au=Isikay,%20Sevcan&rft.date=2021&rft.volume=58&rft.issue=5&rft.spage=1149&rft.epage=1161&rft.pages=1149-1161&rft.issn=1015-8634&rft_id=info:doi/&rft_dat=%3Ckisti%3EJAKO202128557369139%3C/kisti%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true