On reduced Arakelov divisors of real quadratic fields
We generalize the concept of reduced Arakelov divisors and define \(C\)-reduced divisors for a given number \(C \geq 1\). These \(C\)-reduced divisors have remarkable properties which are similar to the properties of reduced ones. In this paper, we describe an algorithm to test whether an Arakelov d...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2016-05 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | Tran, Ha Thanh Nguyen |
| description | We generalize the concept of reduced Arakelov divisors and define \(C\)-reduced divisors for a given number \(C \geq 1\). These \(C\)-reduced divisors have remarkable properties which are similar to the properties of reduced ones. In this paper, we describe an algorithm to test whether an Arakelov divisor of a real quadratic field \(F\) is \(C\)-reduced in time polynomial in \(\log|\Delta_F|\) with \(\Delta_F\) the discriminant of \(F\). Moreover, we give an example of a cubic field for which our algorithm does not work. |
| doi_str_mv | 10.48550/arxiv.1412.5043 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_1412_5043</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2081024399</sourcerecordid><originalsourceid>FETCH-LOGICAL-a519-ec70c778ca2badfc97fcbeb1d37a1c027638b2ebaf1197d7fd454d877be3dcd03</originalsourceid><addsrcrecordid>eNotjztrwzAUhUWh0JBm71QEne3qGcljCH1BIEt2c6UrgVI3TqTYtP--TtPpDOfjcD5CHjirldWaPUP-TmPNFRe1ZkrekJmQkldWCXFHFqXsGWNiaYTWckb09kBzwMEHpKsMn6HrR4ppTKXPhfZxKqGjpwEwwzl5GlPosNyT2whdCYv_nJPd68tu_V5ttm8f69WmAs2bKnjDvDHWg3CA0TcmehccR2mAeybMUlongoPIeWPQRFRaoTXGBYkemZyTx-vsn1J7zOkL8k97UWsvahPwdAWOuT8NoZzbfT_kw3SpFcxyJpRsGvkLnJNRcQ</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2081024399</pqid></control><display><type>article</type><title>On reduced Arakelov divisors of real quadratic fields</title><source>arXiv.org</source><source>Free E- Journals</source><creator>Tran, Ha Thanh Nguyen</creator><creatorcontrib>Tran, Ha Thanh Nguyen</creatorcontrib><description>We generalize the concept of reduced Arakelov divisors and define \(C\)-reduced divisors for a given number \(C \geq 1\). These \(C\)-reduced divisors have remarkable properties which are similar to the properties of reduced ones. In this paper, we describe an algorithm to test whether an Arakelov divisor of a real quadratic field \(F\) is \(C\)-reduced in time polynomial in \(\log|\Delta_F|\) with \(\Delta_F\) the discriminant of \(F\). Moreover, we give an example of a cubic field for which our algorithm does not work.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1412.5043</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algorithms ; Fields (mathematics) ; Mathematics - Number Theory ; Number theory ; Polynomials</subject><ispartof>arXiv.org, 2016-05</ispartof><rights>2016. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,780,881,27902</link.rule.ids><backlink>$$Uhttps://doi.org/10.48550/arXiv.1412.5043$$DView paper in arXiv$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.4064/aa8007-2-2016$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink></links><search><creatorcontrib>Tran, Ha Thanh Nguyen</creatorcontrib><title>On reduced Arakelov divisors of real quadratic fields</title><title>arXiv.org</title><description>We generalize the concept of reduced Arakelov divisors and define \(C\)-reduced divisors for a given number \(C \geq 1\). These \(C\)-reduced divisors have remarkable properties which are similar to the properties of reduced ones. In this paper, we describe an algorithm to test whether an Arakelov divisor of a real quadratic field \(F\) is \(C\)-reduced in time polynomial in \(\log|\Delta_F|\) with \(\Delta_F\) the discriminant of \(F\). Moreover, we give an example of a cubic field for which our algorithm does not work.</description><subject>Algorithms</subject><subject>Fields (mathematics)</subject><subject>Mathematics - Number Theory</subject><subject>Number theory</subject><subject>Polynomials</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><sourceid>GOX</sourceid><recordid>eNotjztrwzAUhUWh0JBm71QEne3qGcljCH1BIEt2c6UrgVI3TqTYtP--TtPpDOfjcD5CHjirldWaPUP-TmPNFRe1ZkrekJmQkldWCXFHFqXsGWNiaYTWckb09kBzwMEHpKsMn6HrR4ppTKXPhfZxKqGjpwEwwzl5GlPosNyT2whdCYv_nJPd68tu_V5ttm8f69WmAs2bKnjDvDHWg3CA0TcmehccR2mAeybMUlongoPIeWPQRFRaoTXGBYkemZyTx-vsn1J7zOkL8k97UWsvahPwdAWOuT8NoZzbfT_kw3SpFcxyJpRsGvkLnJNRcQ</recordid><startdate>20160525</startdate><enddate>20160525</enddate><creator>Tran, Ha Thanh Nguyen</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20160525</creationdate><title>On reduced Arakelov divisors of real quadratic fields</title><author>Tran, Ha Thanh Nguyen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a519-ec70c778ca2badfc97fcbeb1d37a1c027638b2ebaf1197d7fd454d877be3dcd03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Algorithms</topic><topic>Fields (mathematics)</topic><topic>Mathematics - Number Theory</topic><topic>Number theory</topic><topic>Polynomials</topic><toplevel>online_resources</toplevel><creatorcontrib>Tran, Ha Thanh Nguyen</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tran, Ha Thanh Nguyen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On reduced Arakelov divisors of real quadratic fields</atitle><jtitle>arXiv.org</jtitle><date>2016-05-25</date><risdate>2016</risdate><eissn>2331-8422</eissn><abstract>We generalize the concept of reduced Arakelov divisors and define \(C\)-reduced divisors for a given number \(C \geq 1\). These \(C\)-reduced divisors have remarkable properties which are similar to the properties of reduced ones. In this paper, we describe an algorithm to test whether an Arakelov divisor of a real quadratic field \(F\) is \(C\)-reduced in time polynomial in \(\log|\Delta_F|\) with \(\Delta_F\) the discriminant of \(F\). Moreover, we give an example of a cubic field for which our algorithm does not work.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1412.5043</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2016-05 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_arxiv_primary_1412_5043 |
| source | arXiv.org; Free E- Journals |
| subjects | Algorithms Fields (mathematics) Mathematics - Number Theory Number theory Polynomials |
| title | On reduced Arakelov divisors 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=2025-02-02T02%3A17%3A52IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20reduced%20Arakelov%20divisors%20of%20real%20quadratic%20fields&rft.jtitle=arXiv.org&rft.au=Tran,%20Ha%20Thanh%20Nguyen&rft.date=2016-05-25&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1412.5043&rft_dat=%3Cproquest_arxiv%3E2081024399%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2081024399&rft_id=info:pmid/&rfr_iscdi=true |