{"id":"https://openalex.org/W1964915197","doi":"https://doi.org/10.1090/s0025-5718-08-02136-4","title":"Congruences for the Ramanujan function and generalized class numbers","display_name":"Congruences for the Ramanujan function and generalized class numbers","publication_year":2008,"publication_date":"2008-10-14","ids":{"openalex":"https://openalex.org/W1964915197","doi":"https://doi.org/10.1090/s0025-5718-08-02136-4","mag":"1964915197"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02136-4","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02136-4/S0025-5718-08-02136-4.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_indexed_in_scopus":true,"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},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02136-4/S0025-5718-08-02136-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015562884","display_name":"Bernhard Heim","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Bernhard Heim","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Mathematik; Vivatsgasse 7 53111 Bonn Germany"],"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Mathematik; Vivatsgasse 7 53111 Bonn Germany","institution_ids":["https://openalex.org/I4210119712"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015562884"],"corresponding_institution_ids":["https://openalex.org/I4210119712"],"apc_list":null,"apc_paid":null,"fwci":1.233,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":3,"citation_normalized_percentile":{"value":0.419517,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":74,"max":76},"biblio":{"volume":"78","issue":"265","first_page":"431","last_page":"431"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9997,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9997,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9997,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9993,"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/congruence-relation","display_name":"Congruence relation","score":0.9679655},{"id":"https://openalex.org/keywords/congruence","display_name":"Congruence (geometry)","score":0.5942181},{"id":"https://openalex.org/keywords/ramanujan-tau-function","display_name":"Ramanujan tau function","score":0.41193748}],"concepts":[{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.9679655},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.89921105},{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.89479935},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6990522},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.5942181},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.48964578},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4738453},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45266235},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42978856},{"id":"https://openalex.org/C127808406","wikidata":"https://www.wikidata.org/wiki/Q3535240","display_name":"Ramanujan tau function","level":3,"score":0.41193748},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.048887104},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02136-4","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02136-4/S0025-5718-08-02136-4.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_indexed_in_scopus":true,"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},{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.8055","pdf_url":"http://www.ams.org/mcom/2009-78-265/S0025-5718-08-02136-4/S0025-5718-08-02136-4.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02136-4","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02136-4/S0025-5718-08-02136-4.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_indexed_in_scopus":true,"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},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":10,"referenced_works":["https://openalex.org/W1494783320","https://openalex.org/W1569990823","https://openalex.org/W1596766872","https://openalex.org/W1855918773","https://openalex.org/W1993515438","https://openalex.org/W2016612465","https://openalex.org/W2047620811","https://openalex.org/W2061107511","https://openalex.org/W2950812440","https://openalex.org/W3022821551"],"related_works":["https://openalex.org/W4301228773","https://openalex.org/W3215838177","https://openalex.org/W3098271706","https://openalex.org/W2951833366","https://openalex.org/W2945221657","https://openalex.org/W2917145361","https://openalex.org/W2559888834","https://openalex.org/W2084001194","https://openalex.org/W2081852078","https://openalex.org/W2011465559"],"abstract_inverted_index":{"The":[0],"Ramanujan":[1],"$\\tau$-function":[2],"satisfies":[3],"well-known":[4],"congruences":[5,19,50],"modulo":[6],"the":[7,22,45,52],"so-called":[8],"exceptional":[9],"prime":[10],"numbers":[11],"$2,3,5,7,23,691$.":[12],"In":[13],"this":[14],"paper":[15],"we":[16,35],"prove":[17],"new":[18,42],"related":[20,53],"to":[21],"irregular":[23],"primes":[24],"$131$":[25],"and":[26,49],"$593$,":[27],"involving":[28],"generalized":[29],"class":[30],"numbers.":[31],"As":[32],"an":[33],"application":[34],"obtain":[36,40],"distribution":[37],"results.":[38],"We":[39],"a":[41],"proof":[43],"of":[44,51],"famous":[46],"$691$":[47],"congruence":[48],"Rankin":[54],"L-funtion.":[55]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1964915197","counts_by_year":[],"updated_date":"2025-01-20T19:18:45.128431","created_date":"2016-06-24"}