Coding of geodesics on some modular surfaces and applications to odd and even continued fractions
The connection between geodesics on the modular surface PSL(2,Z)∖H and regular continued fractions, established by Series, is extended to a connection between geodesics on Γ∖H and odd and grotesque continued fractions, where Γ≅Z3∗Z3 is the index two subgroup of PSL(2,Z) generated by the order three...
Gespeichert in:
| Veröffentlicht in: | Indagationes mathematicae 2018-10, Vol.29 (5), p.1214-1234 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1234 |
|---|---|
| container_issue | 5 |
| container_start_page | 1214 |
| container_title | Indagationes mathematicae |
| container_volume | 29 |
| creator | Boca, Florin P. Merriman, Claire |
| description | The connection between geodesics on the modular surface PSL(2,Z)∖H and regular continued fractions, established by Series, is extended to a connection between geodesics on Γ∖H and odd and grotesque continued fractions, where Γ≅Z3∗Z3 is the index two subgroup of PSL(2,Z) generated by the order three elements 0−111 and 01−11, and having an ideal quadrilateral as fundamental domain.A similar connection between geodesics on Θ∖H and even continued fractions is discussed in our framework, where Θ denotes the Theta subgroup of PSL(2,Z) generated by 0−110 and 1201. |
| doi_str_mv | 10.1016/j.indag.2018.05.004 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2130280965</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0019357718301988</els_id><sourcerecordid>2130280965</sourcerecordid><originalsourceid>FETCH-LOGICAL-c442t-1164fffcb800d45ab2a0c73cdbc7e098314cdae6a9caa8675c112807a3474663</originalsourceid><addsrcrecordid>eNp9kE1LAzEQhoMoWD9-gZeA510n-5FsDx6k-AWCl97DdDJbUtqkJrsF_71r69nTMMPzzgyPEHcKSgVKP2xKHxyuywpUV0JbAjRnYqY6UxVaAZyLGYCaF3VrzKW4ynkztQYqPRO4iM6HtYy9XHN0nD1lGYPMccdyF924xSTzmHokzhKDk7jfbz3h4GPIcogyOnec84GDpBgGH0Z2sk9IR-ZGXPS4zXz7V6_F8uV5uXgrPj5f3xdPHwU1TTUUSumm73tadQCuaXFVIZCpya3IMMy7WjXkkDXOCbHTpiWlqg4M1o1ptK6vxf1p7T7Fr5HzYDdxTGG6aCtVw4TOdTtR9YmiFHNO3Nt98jtM31aB_VVpN_ao0v6qtNDaSeWUejylePr_4DnZTJ4DsfOJabAu-n_zP3sWfmE</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2130280965</pqid></control><display><type>article</type><title>Coding of geodesics on some modular surfaces and applications to odd and even continued fractions</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>ScienceDirect Journals (5 years ago - present)</source><creator>Boca, Florin P. ; Merriman, Claire</creator><creatorcontrib>Boca, Florin P. ; Merriman, Claire</creatorcontrib><description>The connection between geodesics on the modular surface PSL(2,Z)∖H and regular continued fractions, established by Series, is extended to a connection between geodesics on Γ∖H and odd and grotesque continued fractions, where Γ≅Z3∗Z3 is the index two subgroup of PSL(2,Z) generated by the order three elements 0−111 and 01−11, and having an ideal quadrilateral as fundamental domain.A similar connection between geodesics on Θ∖H and even continued fractions is discussed in our framework, where Θ denotes the Theta subgroup of PSL(2,Z) generated by 0−110 and 1201.</description><identifier>ISSN: 0019-3577</identifier><identifier>EISSN: 1872-6100</identifier><identifier>DOI: 10.1016/j.indag.2018.05.004</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Coding theory ; Even continued fractions ; Fractions ; Geodesics coding ; Geodesy ; Modular surface ; Number theory ; Odd continued fractions ; Quadrilaterals ; Subgroups ; Theorems</subject><ispartof>Indagationes mathematicae, 2018-10, Vol.29 (5), p.1214-1234</ispartof><rights>2018 Royal Dutch Mathematical Society (KWG)</rights><rights>Copyright Elsevier Science Ltd. 2018</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c442t-1164fffcb800d45ab2a0c73cdbc7e098314cdae6a9caa8675c112807a3474663</citedby><cites>FETCH-LOGICAL-c442t-1164fffcb800d45ab2a0c73cdbc7e098314cdae6a9caa8675c112807a3474663</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.indag.2018.05.004$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3548,27923,27924,45994</link.rule.ids></links><search><creatorcontrib>Boca, Florin P.</creatorcontrib><creatorcontrib>Merriman, Claire</creatorcontrib><title>Coding of geodesics on some modular surfaces and applications to odd and even continued fractions</title><title>Indagationes mathematicae</title><description>The connection between geodesics on the modular surface PSL(2,Z)∖H and regular continued fractions, established by Series, is extended to a connection between geodesics on Γ∖H and odd and grotesque continued fractions, where Γ≅Z3∗Z3 is the index two subgroup of PSL(2,Z) generated by the order three elements 0−111 and 01−11, and having an ideal quadrilateral as fundamental domain.A similar connection between geodesics on Θ∖H and even continued fractions is discussed in our framework, where Θ denotes the Theta subgroup of PSL(2,Z) generated by 0−110 and 1201.</description><subject>Coding theory</subject><subject>Even continued fractions</subject><subject>Fractions</subject><subject>Geodesics coding</subject><subject>Geodesy</subject><subject>Modular surface</subject><subject>Number theory</subject><subject>Odd continued fractions</subject><subject>Quadrilaterals</subject><subject>Subgroups</subject><subject>Theorems</subject><issn>0019-3577</issn><issn>1872-6100</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWD9-gZeA510n-5FsDx6k-AWCl97DdDJbUtqkJrsF_71r69nTMMPzzgyPEHcKSgVKP2xKHxyuywpUV0JbAjRnYqY6UxVaAZyLGYCaF3VrzKW4ynkztQYqPRO4iM6HtYy9XHN0nD1lGYPMccdyF924xSTzmHokzhKDk7jfbz3h4GPIcogyOnec84GDpBgGH0Z2sk9IR-ZGXPS4zXz7V6_F8uV5uXgrPj5f3xdPHwU1TTUUSumm73tadQCuaXFVIZCpya3IMMy7WjXkkDXOCbHTpiWlqg4M1o1ptK6vxf1p7T7Fr5HzYDdxTGG6aCtVw4TOdTtR9YmiFHNO3Nt98jtM31aB_VVpN_ao0v6qtNDaSeWUejylePr_4DnZTJ4DsfOJabAu-n_zP3sWfmE</recordid><startdate>20181001</startdate><enddate>20181001</enddate><creator>Boca, Florin P.</creator><creator>Merriman, Claire</creator><general>Elsevier B.V</general><general>Elsevier Science Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20181001</creationdate><title>Coding of geodesics on some modular surfaces and applications to odd and even continued fractions</title><author>Boca, Florin P. ; Merriman, Claire</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c442t-1164fffcb800d45ab2a0c73cdbc7e098314cdae6a9caa8675c112807a3474663</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Coding theory</topic><topic>Even continued fractions</topic><topic>Fractions</topic><topic>Geodesics coding</topic><topic>Geodesy</topic><topic>Modular surface</topic><topic>Number theory</topic><topic>Odd continued fractions</topic><topic>Quadrilaterals</topic><topic>Subgroups</topic><topic>Theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Boca, Florin P.</creatorcontrib><creatorcontrib>Merriman, Claire</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Indagationes mathematicae</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Boca, Florin P.</au><au>Merriman, Claire</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Coding of geodesics on some modular surfaces and applications to odd and even continued fractions</atitle><jtitle>Indagationes mathematicae</jtitle><date>2018-10-01</date><risdate>2018</risdate><volume>29</volume><issue>5</issue><spage>1214</spage><epage>1234</epage><pages>1214-1234</pages><issn>0019-3577</issn><eissn>1872-6100</eissn><abstract>The connection between geodesics on the modular surface PSL(2,Z)∖H and regular continued fractions, established by Series, is extended to a connection between geodesics on Γ∖H and odd and grotesque continued fractions, where Γ≅Z3∗Z3 is the index two subgroup of PSL(2,Z) generated by the order three elements 0−111 and 01−11, and having an ideal quadrilateral as fundamental domain.A similar connection between geodesics on Θ∖H and even continued fractions is discussed in our framework, where Θ denotes the Theta subgroup of PSL(2,Z) generated by 0−110 and 1201.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.indag.2018.05.004</doi><tpages>21</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0019-3577 |
| ispartof | Indagationes mathematicae, 2018-10, Vol.29 (5), p.1214-1234 |
| issn | 0019-3577 1872-6100 |
| language | eng |
| recordid | cdi_proquest_journals_2130280965 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; ScienceDirect Journals (5 years ago - present) |
| subjects | Coding theory Even continued fractions Fractions Geodesics coding Geodesy Modular surface Number theory Odd continued fractions Quadrilaterals Subgroups Theorems |
| title | Coding of geodesics on some modular surfaces and applications to odd and even continued fractions |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-12T10%3A12%3A14IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Coding%20of%20geodesics%20on%20some%20modular%20surfaces%20and%20applications%20to%20odd%20and%20even%20continued%20fractions&rft.jtitle=Indagationes%20mathematicae&rft.au=Boca,%20Florin%20P.&rft.date=2018-10-01&rft.volume=29&rft.issue=5&rft.spage=1214&rft.epage=1234&rft.pages=1214-1234&rft.issn=0019-3577&rft.eissn=1872-6100&rft_id=info:doi/10.1016/j.indag.2018.05.004&rft_dat=%3Cproquest_cross%3E2130280965%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2130280965&rft_id=info:pmid/&rft_els_id=S0019357718301988&rfr_iscdi=true |