{"id":"https://openalex.org/W2008903262","doi":"https://doi.org/10.1090/s0025-5718-01-01341-2","title":"Comparison of algorithms to calculate quadratic irregularity of prime numbers","display_name":"Comparison of algorithms to calculate quadratic irregularity of prime numbers","publication_year":2001,"publication_date":"2001-08-03","ids":{"openalex":"https://openalex.org/W2008903262","doi":"https://doi.org/10.1090/s0025-5718-01-01341-2","mag":"2008903262"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-01-01341-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01341-2","pdf_url":"https://www.ams.org/mcom/2002-71-238/S0025-5718-01-01341-2/S0025-5718-01-01341-2.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/2002-71-238/S0025-5718-01-01341-2/S0025-5718-01-01341-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043053001","display_name":"Joshua Holden","orcid":"https://orcid.org/0000-0003-2847-3777"},"institutions":[{"id":"https://openalex.org/I192578771","display_name":"Rose\u2013Hulman Institute of Technology","ror":"https://ror.org/00mp6e841","country_code":"US","type":"education","lineage":["https://openalex.org/I192578771"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Joshua Holden","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Massachusetts at Amherst, Amherst, Massachusetts 01003","Department of Mathematics, Rose-Hulman Institute of Technology, 5500 Wabash Ave., Terre Haute, Indiana 47803"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Massachusetts at Amherst, Amherst, Massachusetts 01003","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, Rose-Hulman Institute of Technology, 5500 Wabash Ave., Terre Haute, Indiana 47803","institution_ids":["https://openalex.org/I192578771"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043053001"],"corresponding_institution_ids":["https://openalex.org/I192578771"],"apc_list":null,"apc_paid":null,"fwci":0.9641,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.71644936,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"238","first_page":"863","last_page":"871"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.9991999864578247,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9940000176429749,"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":0.8782793283462524},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6498399376869202},{"id":"https://openalex.org/keywords/bernoulli-number","display_name":"Bernoulli number","score":0.6341010928153992},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5815038681030273},{"id":"https://openalex.org/keywords/quadratic-field","display_name":"Quadratic field","score":0.5460432171821594},{"id":"https://openalex.org/keywords/quadratic-residue","display_name":"Quadratic residue","score":0.5305856466293335},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.5301540493965149},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.508752167224884},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4717698097229004},{"id":"https://openalex.org/keywords/modular-form","display_name":"Modular form","score":0.46201789379119873},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.4447348117828369},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.4351067543029785},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39293473958969116},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.37269115447998047},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36752429604530334},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2607603073120117},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.119142085313797}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8782793283462524},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6498399376869202},{"id":"https://openalex.org/C129960964","wikidata":"https://www.wikidata.org/wiki/Q694114","display_name":"Bernoulli number","level":2,"score":0.6341010928153992},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5815038681030273},{"id":"https://openalex.org/C95136341","wikidata":"https://www.wikidata.org/wiki/Q625519","display_name":"Quadratic field","level":4,"score":0.5460432171821594},{"id":"https://openalex.org/C12817185","wikidata":"https://www.wikidata.org/wiki/Q878259","display_name":"Quadratic residue","level":2,"score":0.5305856466293335},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.5301540493965149},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.508752167224884},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4717698097229004},{"id":"https://openalex.org/C75764964","wikidata":"https://www.wikidata.org/wiki/Q870797","display_name":"Modular form","level":2,"score":0.46201789379119873},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.4447348117828369},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.4351067543029785},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39293473958969116},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.37269115447998047},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36752429604530334},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2607603073120117},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.119142085313797}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1090/s0025-5718-01-01341-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01341-2","pdf_url":"https://www.ams.org/mcom/2002-71-238/S0025-5718-01-01341-2/S0025-5718-01-01341-2.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:scholar.rose-hulman.edu:math_fac-1114","is_oa":false,"landing_page_url":"http://libproxy.rose-hulman.edu:2114/journals/mcom/2002-71-238/S0025-5718-01-01341-2/home.html","pdf_url":null,"source":{"id":"https://openalex.org/S4377196619","display_name":"Rose-Hulman Scholar (Rose\u2013Hulman Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I192578771","host_organization_name":"Rose\u2013Hulman Institute of Technology","host_organization_lineage":["https://openalex.org/I192578771"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications - Mathematics","raw_type":"text"},{"id":"pmh:oai:scholarworks.umass.edu:micro_faculty_pubs-1045","is_oa":false,"landing_page_url":"https://scholarworks.umass.edu/micro_faculty_pubs/46","pdf_url":null,"source":{"id":"https://openalex.org/S4306402240","display_name":"ScholarWorks@UMassAmherst (University of Massachusetts Amherst)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I24603500","host_organization_name":"University of Massachusetts Amherst","host_organization_lineage":["https://openalex.org/I24603500"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Microbiology Department Faculty Publication Series","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.2832","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.2832","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/2002-71-238/S0025-5718-01-01341-2/S0025-5718-01-01341-2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.88.2967","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.88.2967","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.rose-hulman.edu/~holden/Preprints/Published/mathcomp02-pub.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.93.4796","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.93.4796","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.rose-hulman.edu/~holden/Preprints/torontopost.pdf","raw_type":"text"},{"id":"pmh:oai:scholarworks.umass.edu:20.500.14394/35298","is_oa":false,"landing_page_url":"https://hdl.handle.net/20.500.14394/35298","pdf_url":null,"source":{"id":"https://openalex.org/S4306402057","display_name":"Scholarworks (University of Massachusetts Amherst)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I24603500","host_organization_name":"University of Massachusetts Amherst","host_organization_lineage":["https://openalex.org/I24603500"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"published","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01341-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01341-2","pdf_url":"https://www.ams.org/mcom/2002-71-238/S0025-5718-01-01341-2/S0025-5718-01-01341-2.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/W2008903262.pdf","grobid_xml":"https://content.openalex.org/works/W2008903262.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W66445618","https://openalex.org/W1495550473","https://openalex.org/W1539838954","https://openalex.org/W1788335386","https://openalex.org/W1980863003","https://openalex.org/W1993515438","https://openalex.org/W2080821937","https://openalex.org/W2106413905","https://openalex.org/W2499325432"],"related_works":["https://openalex.org/W3114165991","https://openalex.org/W2525961875","https://openalex.org/W4226136258","https://openalex.org/W2556431797","https://openalex.org/W4315588443","https://openalex.org/W2256733877","https://openalex.org/W2106050716","https://openalex.org/W1985532317","https://openalex.org/W2380027749","https://openalex.org/W2008903262"],"abstract_inverted_index":{"In":[0,88],"previous":[1],"work,":[2],"the":[3,7,15,44,47,89,135,153,167,176],"author":[4,141],"has":[5],"extended":[6],"concept":[8],"of":[9,17,46,137,152,178,203],"regular":[10],"and":[11,129,165],"irregular":[12],"primes":[13],"to":[14,144,174],"setting":[16],"arbitrary":[18],"totally":[19],"real":[20,113],"number":[21],"fields":[22],"<inline-formula":[23,50,92,179],"content-type=\"math/mathml\">":[24,51,93,180],"<mml:math":[25,52,94,181],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[26,53,95,182],"alttext=\"k":[27,96,183],"0\">":[28,57,97,184],"<mml:semantics>":[29,58,98,185],"<mml:msub>":[30,59,65,99,186],"<mml:mi>k</mml:mi>":[31,66,100,187],"<mml:mrow":[32,63,67,101,188],"class=\"MJX-TeXAtom-ORD\">":[33,64,68,102,189],"<mml:mn>0</mml:mn>":[34,69,103,190],"</mml:mrow>":[35,70,72,104,191],"</mml:msub>":[36,71,73,105,192],"<mml:annotation":[37,74,106,193],"encoding=\"application/x-tex\">k_{0}</mml:annotation>":[38,107,194],"</mml:semantics>":[39,77,108,195],"</mml:math>":[40,78,109,196],"</inline-formula>":[41,79,110,197],",":[42],"using":[43,125,172],"values":[45],"zeta":[48],"function":[49],"alttext=\"zeta":[54],"Subscript":[55],"k":[56],"<mml:mi>":[60],"\u03b6":[61],"</mml:mi>":[62],"encoding=\"application/x-tex\">\\zeta":[75],"_{k_{0}}</mml:annotation>":[76],"at":[80],"negative":[81],"integers":[82],"as":[83],"our":[84],"\u201chigher":[85],"Bernoulli":[86],"numbers\u201d.":[87],"case":[90],"where":[91],"is":[111,132],"a":[112,204],"quadratic":[114],"field,":[115],"Siegel":[116],"presented":[117],"two":[118],"formulas":[119,164],"for":[120,148],"calculating":[121],"these":[122,163],"zeta-values:":[123],"one":[124,130],"entirely":[126],"elementary":[127],"methods":[128],"which":[131],"derived":[133],"from":[134],"theory":[136],"modular":[138],"forms.":[139],"(The":[140],"would":[142],"like":[143],"thank":[145],"Henri":[146],"Cohen":[147],"suggesting":[149],"an":[150],"analysis":[151],"second":[154],"formula.)":[155],"We":[156],"briefly":[157],"discuss":[158],"several":[159],"algorithms":[160],"based":[161],"on":[162],"compare":[166],"running":[168],"time":[169],"involved":[170],"in":[171],"them":[173],"determine":[175],"index":[177],"-irregularity":[198],"(more":[199],"generally,":[200],"\u201cquadratic":[201],"irregularity\u201d)":[202],"prime":[205],"number.":[206]},"counts_by_year":[],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}