{"id":"https://openalex.org/W2467243612","doi":"https://doi.org/10.1090/mcom/3281","title":"Explicit bounds for generators of the class group","display_name":"Explicit bounds for generators of the class group","publication_year":2017,"publication_date":"2017-04-20","ids":{"openalex":"https://openalex.org/W2467243612","doi":"https://doi.org/10.1090/mcom/3281","mag":"2467243612"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3281","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3281","pdf_url":null,"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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1607.02430","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038814844","display_name":"Lo\u00efc Greni\u00e9","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lo\u00efc Greni\u00e9","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5002104488","display_name":"Giuseppe Molteni","orcid":"https://orcid.org/0000-0003-3323-4383"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giuseppe Molteni","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00c3\u00a0 di Milano, via Saldini 50, 20133 Milano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00c3\u00a0 di Milano, via Saldini 50, 20133 Milano, Italy","institution_ids":["https://openalex.org/I189158943"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.04607177,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"87","issue":"313","first_page":"2483","last_page":"2511"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9994000196456909,"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"}},{"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/T11130","display_name":"Coding theory and cryptography","score":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6821714639663696},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6603013873100281},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.521840512752533},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.4891970157623291},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.46024152636528015},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17418819665908813}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6821714639663696},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6603013873100281},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.521840512752533},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.4891970157623291},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.46024152636528015},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17418819665908813}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/mcom/3281","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3281","pdf_url":null,"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:arXiv.org:1607.02430","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.02430","pdf_url":"https://arxiv.org/pdf/1607.02430","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"},{"id":"pmh:oai:air.unimi.it:2434/574122","is_oa":true,"landing_page_url":"http://hdl.handle.net/2434/574122","pdf_url":null,"source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:aisberg.unibg.it:10446/109841","is_oa":false,"landing_page_url":"http://hdl.handle.net/10446/109841","pdf_url":null,"source":{"id":"https://openalex.org/S4377196347","display_name":"Aisberg (University of Bergamo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I11039511","host_organization_name":"University of Bergamo","host_organization_lineage":["https://openalex.org/I11039511"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1607.02430","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.02430","pdf_url":"https://arxiv.org/pdf/1607.02430","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":[{"id":"https://metadata.un.org/sdg/10","score":0.6600000262260437,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W23855251","https://openalex.org/W1223570327","https://openalex.org/W1535615078","https://openalex.org/W1551090076","https://openalex.org/W1558606648","https://openalex.org/W2011809718","https://openalex.org/W2024731156","https://openalex.org/W2074910438","https://openalex.org/W2076928530","https://openalex.org/W2280036466","https://openalex.org/W2484413702","https://openalex.org/W3007836994","https://openalex.org/W4235110860","https://openalex.org/W4292101538","https://openalex.org/W4293193836"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Assuming":[0],"Generalized":[1],"Riemann\u2019s":[2],"Hypothesis,":[3],"Bach":[4],"proved":[5],"that":[6,287,353],"the":[7,240,244,268],"class":[8],"group":[9],"<inline-formula":[10,59,89,139,206,247,289,354],"content-type=\"math/mathml\">":[11,60,90,140,207,248,290,355],"<mml:math":[12,61,91,141,208,249,291,356],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[13,62,92,142,209,250,292,357],"alttext=\"script":[14,293,358],"upper":[15,21,64,97,101,154,158,211,215,252,294,300,359,365],"C":[16,295,360],"script":[17,296,361],"l":[18,297,362],"Subscript":[19,99,156,213,298,363],"bold":[20,100,157,214,299,364],"K\">":[22,65,102,159,216,253,301,366],"<mml:semantics>":[23,66,103,160,217,254,302,367],"<mml:mrow>":[24,104,161,303,368],"<mml:mrow":[25,37,39,67,118,120,186,188,223,225,255,304,316,318,369,381,383],"class=\"MJX-TeXAtom-ORD\">":[26,38,40,68,119,121,187,189,224,226,256,305,317,319,370,382,384],"<mml:mi":[27,41,69,114,122,182,190,219,227,257,306,320,371,385],"class=\"MJX-tex-caligraphic\"":[28,307,372],"mathvariant=\"script\">C</mml:mi>":[29,308,373],"</mml:mrow>":[30,43,44,46,71,124,125,127,192,193,195,229,230,259,309,322,323,325,374,387,388,390],"<mml:mspace":[31,310,375],"width=\"negativethinmathspace\"/>":[32,311,376],"<mml:msub>":[33,113,181,218,312,377],"<mml:mi>":[34,313,378],"\u2113":[35,314,379],"</mml:mi>":[36,117,185,222,315,380],"mathvariant=\"bold\">K</mml:mi>":[42,70,123,191,228,258,321,386],"</mml:msub>":[45,126,194,231,324,389],"<mml:annotation":[47,72,128,196,232,260,326],"encoding=\"application/x-tex\">\\mathcal":[48,327],"C\\!\\ell":[49,328],"_{\\mathbf":[50,131,199,234,329],"{K}}</mml:annotation>":[51,132,200,235,330],"</mml:semantics>":[52,75,133,201,236,263,331],"</mml:math>":[53,76,134,202,237,264,332],"</inline-formula>":[54,77,135,203,238,265,333],"of":[55,243,246,284],"a":[56,278,282],"number":[57],"field":[58],"alttext=\"bold":[63,251],"encoding=\"application/x-tex\">\\mathbf":[73,261],"{K}</mml:annotation>":[74,262],"may":[78],"be":[79],"generated":[80],"using":[81],"prime":[82,285],"ideals":[83,286],"whose":[84],"norm":[85],"is":[86,239,345],"bounded":[87],"by":[88,138],"alttext=\"12":[93],"log":[94,151],"squared":[95,152],"normal":[96,153],"Delta":[98,155,212],"<mml:mn>12</mml:mn>":[105],"<mml:msup>":[106,174],"<mml:mi>log</mml:mi>":[107,175],"<mml:mn>2</mml:mn>":[108,176],"</mml:msup>":[109,177],"<mml:mo>":[110,178],"\u2061":[111,179],"</mml:mo>":[112,180],"mathvariant=\"normal\">":[115,183,220],"\u0394":[116,184,221],"encoding=\"application/x-tex\">12\\log":[129],"^2\\Delta":[130,198],",":[136],"and":[137,275,334],"alttext=\"left-parenthesis":[143],"4":[144],"plus":[145],"o":[146],"left-parenthesis":[147],"1":[148],"right-parenthesis":[149,150],"<mml:mo":[162,167,170,172],"stretchy=\"false\">(</mml:mo>":[163,168],"<mml:mn>4</mml:mn>":[164],"<mml:mo>+</mml:mo>":[165],"<mml:mi>o</mml:mi>":[166],"<mml:mn>1</mml:mn>":[169],"stretchy=\"false\">)</mml:mo>":[171,173],"encoding=\"application/x-tex\">(4+o(1))\\log":[197],"asymptotically,":[204],"where":[205],"alttext=\"normal":[210],"encoding=\"application/x-tex\">\\Delta":[233],"absolute":[241],"value":[242],"discriminant":[245],".":[266],"Under":[267],"same":[269],"assumption,":[270],"Belabas,":[271],"Diaz":[272,274],"y":[273],"Friedman":[276],"showed":[277],"way":[279],"to":[280],"determine":[281],"set":[283],"generates":[288],"which":[335,344],"performs":[336],"better":[337],"than":[338],"Bach\u2019s":[339],"bound":[340],"in":[341],"computations,":[342],"but":[343],"asymptotically":[346],"worse.":[347],"In":[348],"this":[349],"paper":[350],"we":[351],"show":[352],"<mml:annota":[391]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
