{"id":"https://openalex.org/W2064619631","doi":"https://doi.org/10.1090/s0025-5718-05-01758-8","title":"Point counting on Picard curves in large characteristic","display_name":"Point counting on Picard curves in large characteristic","publication_year":2005,"publication_date":"2005-03-31","ids":{"openalex":"https://openalex.org/W2064619631","doi":"https://doi.org/10.1090/s0025-5718-05-01758-8","mag":"2064619631"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-05-01758-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01758-8","pdf_url":"https://www.ams.org/mcom/2005-74-252/S0025-5718-05-01758-8/S0025-5718-05-01758-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2005-74-252/S0025-5718-05-01758-8/S0025-5718-05-01758-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074360205","display_name":"Mark Bauer","orcid":null},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Mark Bauer","raw_affiliation_strings":["University of Calgary, Department of Mathematics and Statistics, 2500 University Dr. NW, Calgary, Alberta, Canada T2N 1N4"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Calgary, Department of Mathematics and Statistics, 2500 University Dr. NW, Calgary, Alberta, Canada T2N 1N4","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003024529","display_name":"Edlyn Teske","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Edlyn Teske","raw_affiliation_strings":["University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario, Canada N2L 3G1"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario, Canada N2L 3G1","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014704518","display_name":"Annegret Weng","orcid":"https://orcid.org/0000-0002-6932-5052"},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Annegret Weng","raw_affiliation_strings":["Johannes Gutenberg-Universit\u00c3\u00a4t, Fachbereich Mathematik, Staudingerweg 9, 55128 Mainz, Germany","Johannes Gutenberg-Universit\u00e4t, Fachbereich Mathematik, Staudingerweg 9, 55128 Mainz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johannes Gutenberg-Universit\u00c3\u00a4t, Fachbereich Mathematik, Staudingerweg 9, 55128 Mainz, Germany","institution_ids":["https://openalex.org/I197323543"]},{"raw_affiliation_string":"Johannes Gutenberg-Universit\u00e4t, Fachbereich Mathematik, Staudingerweg 9, 55128 Mainz, Germany","institution_ids":["https://openalex.org/I197323543"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2972,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.89493818,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"74","issue":"252","first_page":"1983","last_page":"2005"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9980000257492065,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9248183965682983},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.7843830585479736},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6591154932975769},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.6049581170082092},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6025828719139099},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5469622015953064},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4454723000526428},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4433761239051819},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36733922362327576},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3188450336456299},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.19425421953201294},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11818239092826843}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9248183965682983},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.7843830585479736},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6591154932975769},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.6049581170082092},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6025828719139099},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5469622015953064},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4454723000526428},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4433761239051819},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36733922362327576},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3188450336456299},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.19425421953201294},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11818239092826843},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-05-01758-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01758-8","pdf_url":"https://www.ams.org/mcom/2005-74-252/S0025-5718-05-01758-8/S0025-5718-05-01758-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.434","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.434","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2005-74-252/S0025-5718-05-01758-8/S0025-5718-05-01758-8.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-05-01758-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01758-8","pdf_url":"https://www.ams.org/mcom/2005-74-252/S0025-5718-05-01758-8/S0025-5718-05-01758-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2064619631.pdf","grobid_xml":"https://content.openalex.org/works/W2064619631.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W145263383","https://openalex.org/W1503579934","https://openalex.org/W1515192744","https://openalex.org/W1522339149","https://openalex.org/W1545876477","https://openalex.org/W1557415002","https://openalex.org/W1575538702","https://openalex.org/W1981455414","https://openalex.org/W1993844643","https://openalex.org/W2006720508","https://openalex.org/W2008272678","https://openalex.org/W2011742510","https://openalex.org/W2019816098","https://openalex.org/W2036117875","https://openalex.org/W2069485873","https://openalex.org/W2073799044","https://openalex.org/W2076178640","https://openalex.org/W2085388238","https://openalex.org/W2089240617","https://openalex.org/W2113759670","https://openalex.org/W2137120266","https://openalex.org/W2156186849","https://openalex.org/W4244916260","https://openalex.org/W4246140522","https://openalex.org/W4249240057","https://openalex.org/W4251630068"],"related_works":["https://openalex.org/W2007405763","https://openalex.org/W3136087161","https://openalex.org/W1486373823","https://openalex.org/W2053762185","https://openalex.org/W2952352711","https://openalex.org/W1909918105","https://openalex.org/W2068656449","https://openalex.org/W2612896625","https://openalex.org/W1955455432","https://openalex.org/W4299961354"],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2],"algorithm":[3,54],"for":[4],"computing":[5],"the":[6,9,21,53],"cardinality":[7],"of":[8,11],"Jacobian":[10],"a":[12,17,25],"random":[13],"Picard":[14],"curve":[15],"over":[16],"finite":[18],"field.":[19],"If":[20],"underlying":[22],"field":[23,27],"is":[24],"prime":[26],"<inline-formula":[28,57],"content-type=\"math/mathml\">":[29,58],"<mml:math":[30,59],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[31,60],"alttext=\"double-struck":[32],"upper":[33],"F":[34],"Subscript":[35],"p\">":[36],"<mml:semantics>":[37,68],"<mml:msub>":[38],"<mml:mrow":[39],"class=\"MJX-TeXAtom-ORD\">":[40],"<mml:mi":[41],"mathvariant=\"double-struck\">F</mml:mi>":[42],"</mml:mrow>":[43,78],"<mml:mi>p</mml:mi>":[44,74],"</mml:msub>":[45],"<mml:annotation":[46,79],"encoding=\"application/x-tex\">\\mathbb":[47],"{F}_p</mml:annotation>":[48],"</mml:semantics>":[49,82],"</mml:math>":[50,83],"</inline-formula>":[51,84],",":[52],"has":[55],"complexity":[56],"alttext=\"upper":[61],"O":[62],"left-parenthesis":[63],"StartRoot":[64],"p":[65],"EndRoot":[66],"right-parenthesis\">":[67],"<mml:mrow>":[69],"<mml:mi>O</mml:mi>":[70],"<mml:mo":[71,76],"stretchy=\"false\">(</mml:mo>":[72],"<mml:msqrt>":[73],"</mml:msqrt>":[75],"stretchy=\"false\">)</mml:mo>":[77],"encoding=\"application/x-tex\">O(\\sqrt":[80],"{p})</mml:annotation>":[81],".":[85]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}