{"id":"https://openalex.org/W2085680875","doi":"https://doi.org/10.1080/10586458.2007.10129011","title":"An Explicit Formula for the Arithmetic\u2013Geometric Mean in Genus 3","display_name":"An Explicit Formula for the Arithmetic\u2013Geometric Mean in Genus 3","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2085680875","doi":"https://doi.org/10.1080/10586458.2007.10129011","mag":"2085680875"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2007.10129011","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2007.10129011","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/math/0403182","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042189359","display_name":"David Lehavi","orcid":"https://orcid.org/0000-0002-8603-5479"},"institutions":[{"id":"https://openalex.org/I264262938","display_name":"K\u0131rklareli University","ror":"https://ror.org/00jb0e673","country_code":"TR","type":"education","lineage":["https://openalex.org/I264262938"]},{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES","TR"],"is_corresponding":true,"raw_author_name":"D. Lehavi","raw_affiliation_strings":["\n Correlix Ltd., 6 Galgaley Haplada Street, POB 12607, Herzelia Pituah, Isreal 46733","Universitat Aut\u00f2noma de Barcelona"],"affiliations":[{"raw_affiliation_string":"\n Correlix Ltd., 6 Galgaley Haplada Street, POB 12607, Herzelia Pituah, Isreal 46733","institution_ids":["https://openalex.org/I264262938"]},{"raw_affiliation_string":"Universitat Aut\u00f2noma de Barcelona","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114026163","display_name":"Christophe Ritzenthaler","orcid":null},"institutions":[{"id":"https://openalex.org/I4210138206","display_name":"Institut de Math\u00e9matiques de Marseille","ror":"https://ror.org/042h2y225","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210138206","https://openalex.org/I4210141950","https://openalex.org/I4210142724"]},{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES","FR"],"is_corresponding":false,"raw_author_name":"C. Ritzenthaler","raw_affiliation_strings":["\n Institut de Math\u00e9matiques de Luminy, 163 Avenue de Luminy, Case 907, 13288 Marseille, France","Universitat Aut\u00f2noma de Barcelona"],"affiliations":[{"raw_affiliation_string":"\n Institut de Math\u00e9matiques de Luminy, 163 Avenue de Luminy, Case 907, 13288 Marseille, France","institution_ids":["https://openalex.org/I4210138206"]},{"raw_affiliation_string":"Universitat Aut\u00f2noma de Barcelona","institution_ids":["https://openalex.org/I123044942"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042189359"],"corresponding_institution_ids":["https://openalex.org/I123044942","https://openalex.org/I264262938"],"apc_list":null,"apc_paid":null,"fwci":1.8185,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.83147915,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"16","issue":"4","first_page":"421","last_page":"440"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9995999932289124,"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":0.9995999932289124,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.8965209722518921},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.7620751261711121},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.7052226662635803},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.6443422436714172},{"id":"https://openalex.org/keywords/geometric-mean","display_name":"Geometric mean","score":0.5719811916351318},{"id":"https://openalex.org/keywords/elliptic-integral","display_name":"Elliptic integral","score":0.49360549449920654},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4698048233985901},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4304155111312866},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3814598619937897},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24577701091766357},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14223003387451172}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8965209722518921},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.7620751261711121},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7052226662635803},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.6443422436714172},{"id":"https://openalex.org/C40222840","wikidata":"https://www.wikidata.org/wiki/Q185049","display_name":"Geometric mean","level":2,"score":0.5719811916351318},{"id":"https://openalex.org/C52704855","wikidata":"https://www.wikidata.org/wiki/Q1126603","display_name":"Elliptic integral","level":2,"score":0.49360549449920654},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4698048233985901},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4304155111312866},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3814598619937897},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24577701091766357},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14223003387451172},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/10586458.2007.10129011","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2007.10129011","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:math/0403182","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0403182","pdf_url":"https://arxiv.org/pdf/math/0403182","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"},{"id":"pmh:oai:CULeuclid:euclid.em/1204836513","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1204836513","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.235.2069","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.2069","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0403182v2.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/0403182","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0403182","pdf_url":"https://arxiv.org/pdf/math/0403182","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":14,"referenced_works":["https://openalex.org/W1534976569","https://openalex.org/W1567236289","https://openalex.org/W1567237434","https://openalex.org/W1622445966","https://openalex.org/W1764048552","https://openalex.org/W1973504462","https://openalex.org/W1995864174","https://openalex.org/W2048002525","https://openalex.org/W2056711647","https://openalex.org/W2090987531","https://openalex.org/W2115819075","https://openalex.org/W2165118609","https://openalex.org/W2318730560","https://openalex.org/W3105033236"],"related_works":["https://openalex.org/W2358906198","https://openalex.org/W2069836761","https://openalex.org/W2378598099","https://openalex.org/W2611275940","https://openalex.org/W2367539883","https://openalex.org/W4236012289","https://openalex.org/W2505482706","https://openalex.org/W2361845322","https://openalex.org/W2030107956","https://openalex.org/W3092473972"],"abstract_inverted_index":{"The":[0,16],"arithmetic--geometric":[1],"mean":[2],"algorithm":[3,18,37],"for":[4,19,38],"calculating":[5],"elliptic":[6],"integrals":[7,21,40],"of":[8,22,41],"the":[9,35],"first":[10],"type":[11],"was":[12,25],"introduced":[13,26],"by":[14,27],"Gauss.":[15],"analogous":[17,36],"abelian":[20,39],"genus":[23,42],"$2$":[24],"Richelot":[28],"(1837)":[29],"and":[30],"Humbert":[31],"(1901).":[32],"We":[33],"present":[34],"3.":[43]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
