{"id":"https://openalex.org/W2760567403","doi":"https://doi.org/10.1080/10586458.2017.1422161","title":"On the Evaluation of Singular Invariants for Canonical Generators of Certain Genus One Arithmetic Groups","display_name":"On the Evaluation of Singular Invariants for Canonical Generators of Certain Genus One Arithmetic Groups","publication_year":2018,"publication_date":"2018-01-25","ids":{"openalex":"https://openalex.org/W2760567403","doi":"https://doi.org/10.1080/10586458.2017.1422161","mag":"2760567403"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2017.1422161","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2017.1422161","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1709.07640","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jay Jorgenson","orcid":null},"institutions":[{"id":"https://openalex.org/I125687163","display_name":"City College of New York","ror":"https://ror.org/00wmhkr98","country_code":"US","type":"education","lineage":["https://openalex.org/I125687163"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jay Jorgenson","raw_affiliation_strings":["Department of Mathematics, The City College of New York, Convent Avenue at 138th Street, New York, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The City College of New York, Convent Avenue at 138th Street, New York, NY, USA","institution_ids":["https://openalex.org/I125687163"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Lejla Smajlovi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I104817121","display_name":"University of Sarajevo","ror":"https://ror.org/02hhwgd43","country_code":"BA","type":"education","lineage":["https://openalex.org/I104817121"]}],"countries":["BA"],"is_corresponding":false,"raw_author_name":"Lejla Smajlovi\u0107","raw_affiliation_strings":["Department of Mathematics, University of Sarajevo, Zmaja od Bosne 35, Sarajevo, Bosnia and Herzegovina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sarajevo, Zmaja od Bosne 35, Sarajevo, Bosnia and Herzegovina","institution_ids":["https://openalex.org/I104817121"]}]},{"author_position":"last","author":{"id":null,"display_name":"Holger Then","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Holger Then","raw_affiliation_strings":["Alemannenweg 1, Giengen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alemannenweg 1, Giengen, Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I125687163"],"apc_list":null,"apc_paid":null,"fwci":0.9717,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69675867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"29","issue":"1","first_page":"1","last_page":"27"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.20579999685287476,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.20579999685287476,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.16110000014305115,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.15080000460147858,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.5867999792098999},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.5759999752044678},{"id":"https://openalex.org/keywords/complex-multiplication","display_name":"Complex multiplication","score":0.5339000225067139},{"id":"https://openalex.org/keywords/ring-of-integers","display_name":"Ring of integers","score":0.5246000289916992},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4846000075340271},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4828999936580658},{"id":"https://openalex.org/keywords/holomorphic-function","display_name":"Holomorphic function","score":0.4683000147342682},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.45730000734329224},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.44040000438690186},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.43230000138282776},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.4212999939918518}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9236999750137329},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.5867999792098999},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.5759999752044678},{"id":"https://openalex.org/C80146680","wikidata":"https://www.wikidata.org/wiki/Q2654923","display_name":"Complex multiplication","level":3,"score":0.5339000225067139},{"id":"https://openalex.org/C164810661","wikidata":"https://www.wikidata.org/wiki/Q1358313","display_name":"Ring of integers","level":3,"score":0.5246000289916992},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4846000075340271},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4828999936580658},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.4683000147342682},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.45730000734329224},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.44040000438690186},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.43230000138282776},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4223000109195709},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.4212999939918518},{"id":"https://openalex.org/C207043602","wikidata":"https://www.wikidata.org/wiki/Q266237","display_name":"Algebraic curve","level":2,"score":0.41670000553131104},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.413100004196167},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.4115000069141388},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3709000051021576},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.36730000376701355},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33489999175071716},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.32120001316070557},{"id":"https://openalex.org/C8367249","wikidata":"https://www.wikidata.org/wiki/Q912083","display_name":"Ideal class group","level":3,"score":0.3190999925136566},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.3188999891281128},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.3111000061035156},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.29739999771118164},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.2955999970436096},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.2946000099182129},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29260000586509705},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C2778795570","wikidata":"https://www.wikidata.org/wiki/Q5508772","display_name":"Function field","level":3,"score":0.2879999876022339},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.28189998865127563},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2809999883174896},{"id":"https://openalex.org/C200917960","wikidata":"https://www.wikidata.org/wiki/Q3847057","display_name":"Singular point of a curve","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C148607811","wikidata":"https://www.wikidata.org/wiki/Q746863","display_name":"Algebraic function","level":3,"score":0.26570001244544983},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.2655999958515167},{"id":"https://openalex.org/C123958593","wikidata":"https://www.wikidata.org/wiki/Q938102","display_name":"Elliptic function","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C27783845","wikidata":"https://www.wikidata.org/wiki/Q5421272","display_name":"Explicit formulae","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C63036529","wikidata":"https://www.wikidata.org/wiki/Q1855669","display_name":"Invariant theory","level":3,"score":0.257099986076355}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10586458.2017.1422161","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2017.1422161","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1709.07640","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.07640","pdf_url":"https://arxiv.org/pdf/1709.07640","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1709.07640","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.07640","pdf_url":"https://arxiv.org/pdf/1709.07640","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W116915404","https://openalex.org/W1526788457","https://openalex.org/W1970580817","https://openalex.org/W1986527929","https://openalex.org/W2025384727","https://openalex.org/W2033796951","https://openalex.org/W2060377935","https://openalex.org/W2244294362","https://openalex.org/W2486418386","https://openalex.org/W4232584877","https://openalex.org/W4244111325"],"related_works":[],"abstract_inverted_index":{"Let":[0],"N":[1,170],"be":[2],"a":[3,17,132,161,188],"positive":[4],"square-free":[5],"integer":[6,46],"such":[7],"that":[8,109],"the":[9,28,53,58,71,75,86,110,123,129,194,209,214],"discrete":[10],"group":[11],"\u03930(N)+":[12,34],"has":[13],"genus":[14],"one.":[15],"In":[16,52,182],"previous":[18],"article,":[19],"we":[20,56,69,107,121,185],"constructed":[21],"canonical":[22],"generators":[23],"xN":[24,64],"and":[25,65,78,114,142,149,171,173],"yN":[26],"of":[27,74,105,126,131,137,139,147,177,190,198,216],"holomorphic":[29],"function":[30],"field":[31,136,197],"associated":[32],"with":[33,45],"as":[35,37,128,220,222],"well":[36],"an":[38,102],"algebraic":[39,117,124],"equation":[40],"PN(xN,":[41],"yN)":[42],"=":[43],"0":[44],"coefficients":[47,201,219],"satisfied":[48],"by":[49,67,157],"these":[50],"generators.":[51],"present":[54],"paper,":[55],"study":[57],"singular":[59],"moduli":[60],"problem":[61],"corresponding":[62],"to":[63,101],"yN,":[66],"which":[68,97],"mean":[70],"arithmetic":[72,175],"nature":[73,125],"numbers":[76,112],"xN(\u03c4)":[77,113,127],"yN(\u03c4)":[79,115],"for":[80,168,193],"any":[81,94],"CM":[82,95],"point":[83,96,104],"\u03c4":[84,92,148],"in":[85],"upper":[87],"half":[88],"plane":[89],"H.":[90],"If":[91],"is":[93,98],"not":[99],"equivalent":[100],"elliptic":[103],"\u03930(N)+,":[106],"prove":[108],"complex":[111],"are":[116,155,166,180,202],"integers.":[118],"Going":[119],"further,":[120],"characterize":[122],"generator":[130],"certain":[133],"ring":[134],"class":[135,196],"Q(\u03c4)":[138],"prescribed":[140],"order":[141],"discriminant":[143],"depending":[144],"on":[145],"properties":[146],"level":[150],"N.":[151],"The":[152],"theoretical":[153],"considerations":[154],"supplemented":[156],"computational":[158],"examples.":[159],"As":[160],"result,":[162],"several":[163],"explicit":[164],"evaluations":[165],"given":[167],"various":[169],"\u03c4,":[172],"further":[174],"consequences":[176],"our":[178],"analysis":[179],"presented.":[181],"one":[183],"example,":[184],"explicitly":[186],"construct":[187],"set":[189],"minimal":[191,210],"polynomials":[192],"Hilbert":[195],"Q(-74)":[199],"whose":[200],"less":[203],"than":[204],"2.2":[205],"\u00d7":[206,224],"104,":[207],"whereas":[208],"polynomial":[211],"obtained":[212],"from":[213],"Hauptmodul":[215],"PSL(2,Z)":[217],"have":[218],"large":[221],"6.6":[223],"1073.":[225]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2017-10-06T00:00:00"}