{"id":"https://openalex.org/W2057300596","doi":"https://doi.org/10.1080/10586458.2003.10504501","title":"Numerical Investigations Related to the Derivatives of the<i>L</i>-Series of Certain Elliptic Curves","display_name":"Numerical Investigations Related to the Derivatives of the<i>L</i>-Series of Certain Elliptic Curves","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2057300596","doi":"https://doi.org/10.1080/10586458.2003.10504501","mag":"2057300596"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2003.10504501","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2003.10504501","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065359721","display_name":"Christophe Delaunay","orcid":"https://orcid.org/0000-0001-8197-2394"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"C. Delaunay","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Facult\u00e9 des sciences de Base, CSAG , 1015 Lausanne, Switzerland E-mail: christophe.delaunay@epfl.ch"],"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Facult\u00e9 des sciences de Base, CSAG , 1015 Lausanne, Switzerland E-mail: christophe.delaunay@epfl.ch","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049598647","display_name":"Sylvain Duquesne","orcid":"https://orcid.org/0000-0002-3854-8253"},"institutions":[{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"S. Duquesne","raw_affiliation_strings":["D\u00e9partement des Sciences Math\u00e9matiques , Universit\u00e9 Montpellier II -Case Courrier 051, Place Eug\u00e8ne Bataillon , 34095 Montpellier cedex 5, France E-mail: duquesne@math.univ-montp2.fr"],"affiliations":[{"raw_affiliation_string":"D\u00e9partement des Sciences Math\u00e9matiques , Universit\u00e9 Montpellier II -Case Courrier 051, Place Eug\u00e8ne Bataillon , 34095 Montpellier cedex 5, France E-mail: duquesne@math.univ-montp2.fr","institution_ids":["https://openalex.org/I19894307"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065359721"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":0.4423,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.60284218,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"12","issue":"3","first_page":"311","last_page":"317"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":1.0,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10849","display_name":"Finite Group Theory Research","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/mathematics","display_name":"Mathematics","score":0.9013193845748901},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.8349938988685608},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.7996269464492798},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7788556814193726},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5976085662841797},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44225162267684937},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4307985305786133},{"id":"https://openalex.org/keywords/supersingular-elliptic-curve","display_name":"Supersingular elliptic curve","score":0.4298315644264221},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.42739415168762207},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3309835195541382},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.050767987966537476}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9013193845748901},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.8349938988685608},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.7996269464492798},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7788556814193726},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5976085662841797},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44225162267684937},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4307985305786133},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.4298315644264221},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.42739415168762207},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3309835195541382},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.050767987966537476},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10586458.2003.10504501","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2003.10504501","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6000000238418579,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W205078255","https://openalex.org/W1496801598","https://openalex.org/W1529471319","https://openalex.org/W1541242269","https://openalex.org/W1848741209","https://openalex.org/W1868013030","https://openalex.org/W1971987731","https://openalex.org/W1976994099","https://openalex.org/W1986432345","https://openalex.org/W2000658662","https://openalex.org/W2006264362","https://openalex.org/W2016499826","https://openalex.org/W2023336105","https://openalex.org/W2037737946","https://openalex.org/W2086711200","https://openalex.org/W2333976070","https://openalex.org/W2592230379","https://openalex.org/W2604330053"],"related_works":["https://openalex.org/W2951225764","https://openalex.org/W3172879256","https://openalex.org/W4389775313","https://openalex.org/W118970476","https://openalex.org/W2039569224","https://openalex.org/W2513246935","https://openalex.org/W1734214274","https://openalex.org/W3120152545","https://openalex.org/W1591034480","https://openalex.org/W1888039291"],"abstract_inverted_index":{"In":[0,64],"[Zagier":[1],"and":[2,27,43,61,88,126],"Kramarz":[3],"87],":[4],"the":[5,8,12,15,35,44,49,54,59,73,91,113,130],"authors":[6],"computed":[7],"critical":[9],"value":[10],"of":[11,14,17,37,46,48,75,93,95,108,121,123],"L-series":[13],"family":[16,74],"elliptic":[18,76],"curves":[19,38,77,94,122],"x":[20],"3":[21,24,97,125],"+":[22],"y":[23],"=":[25],"m":[26],"they":[28],"pointed":[29],"out":[30],"some":[31],"numerical":[32],"phenomena":[33],"concerning":[34],"frequency":[36,45],"with":[39],"a":[40,69,85,104],"positive":[41,106],"rank":[42,55,87,96,114,124],"occurrences":[47],"Tate-Shafarevich":[50],"groups":[51,111],"III":[52,132],"in":[53,112],"0":[56],"case":[57],"(assuming":[58],"Birch":[60],"Swinnerton-Dyer":[62],"conjecture).":[63],"this":[65],"paper,":[66],"we":[67,89,118],"give":[68,119],"similar":[70],"study":[71],"for":[72,128],"associated":[78],"to":[79],"simplest":[80],"cubic":[81],"fields.":[82],"Thesecurves":[83],"have":[84],"nonzero":[86],"discuss":[90],"density":[92,107],"that":[98],"occurs.":[99],"We":[100],"also":[101],"remark":[102],"on":[103],"possible":[105],"nontrivial":[109],"TateShafarevitch":[110],"1":[115],"case.":[116],"Finally,":[117],"examples":[120],"5":[127],"which":[129],"group":[131],"is":[133],"nontrivial.":[134]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
