{"id":"https://openalex.org/W2020887339","doi":"https://doi.org/10.1090/s0025-5718-96-00726-0","title":"Spontaneous generation of modular invariants","display_name":"Spontaneous generation of modular invariants","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2020887339","doi":"https://doi.org/10.1090/s0025-5718-96-00726-0","mag":"2020887339"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-96-00726-0","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00726-0","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110897780","display_name":"Harvey Cohn","orcid":null},"institutions":[{"id":"https://openalex.org/I125687163","display_name":"City College of New York","ror":"https://ror.org/00wmhkr98","country_code":"US","type":"education","lineage":["https://openalex.org/I125687163"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Harvey Cohn","raw_affiliation_strings":["Department of Mathematics, City College (Cuny), New York, New York 10031","IDA, Bowie, Maryland 20715-4300"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City College (Cuny), New York, New York 10031","institution_ids":["https://openalex.org/I125687163"]},{"raw_affiliation_string":"IDA, Bowie, Maryland 20715-4300","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063250125","display_name":"John McKay","orcid":"https://orcid.org/0000-0003-4311-5513"},"institutions":[{"id":"https://openalex.org/I60158472","display_name":"Concordia University","ror":"https://ror.org/0420zvk78","country_code":"CA","type":"education","lineage":["https://openalex.org/I60158472"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"John McKay","raw_affiliation_strings":["Department of Computer Science, Concordia University, Montreal, Quebec, Canada H3G 1M8"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Concordia University, Montreal, Quebec, Canada H3G 1M8","institution_ids":["https://openalex.org/I60158472"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110897780"],"corresponding_institution_ids":["https://openalex.org/I125687163"],"apc_list":null,"apc_paid":null,"fwci":1.5338,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.79365079,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"65","issue":"215","first_page":"1295","last_page":"1309"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","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"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","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"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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":0.9866999983787537,"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/algorithm","display_name":"Algorithm","score":0.6393686532974243},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.5452800393104553},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4644463360309601},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.445085734128952},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4419625401496887},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3723942041397095},{"id":"https://openalex.org/keywords/database","display_name":"Database","score":0.34205305576324463},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.08423426747322083}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6393686532974243},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.5452800393104553},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4644463360309601},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.445085734128952},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4419625401496887},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3723942041397095},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.34205305576324463},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.08423426747322083},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-96-00726-0","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00726-0","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:CiteSeerX.psu:10.1.1.99.3582","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.99.3582","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/1996-65-215/S0025-5718-96-00726-0/S0025-5718-96-00726-0.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W99542110","https://openalex.org/W355015062","https://openalex.org/W1537170074","https://openalex.org/W1964461384","https://openalex.org/W1984666729","https://openalex.org/W1993669867","https://openalex.org/W2000193014","https://openalex.org/W2000658662","https://openalex.org/W2023769891","https://openalex.org/W2033474765","https://openalex.org/W2063490946","https://openalex.org/W2071915949","https://openalex.org/W2320352761","https://openalex.org/W4236077621","https://openalex.org/W4240035337","https://openalex.org/W4244111325"],"related_works":["https://openalex.org/W2361861616","https://openalex.org/W2263699433","https://openalex.org/W2377979023","https://openalex.org/W2218034408","https://openalex.org/W2392921965","https://openalex.org/W2358755282","https://openalex.org/W2625833328","https://openalex.org/W1533177136","https://openalex.org/W4380994516","https://openalex.org/W2556260348"],"abstract_inverted_index":{"It":[0],"is":[1],"possible":[2],"to":[3,252],"compute":[4],"<inline-formula":[5,45,67,83,98,138,155,185,225,258,299,335],"content-type=\"math/mathml\">":[6,46,68,84,99,139,156,186,226,259,300,336],"<mml:math":[7,47,69,85,100,140,157,187,227,260,301,337],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[8,48,70,86,101,141,158,188,228,261,302,338],"alttext=\"j":[9],"left-parenthesis":[10,103,162,192,230,265,306],"tau":[11,163,194,345],"right-parenthesis\">":[12,164,195,234,311,346],"<mml:semantics>":[13,51,72,88,110,144,165,196,235,272,312,347],"<mml:mrow>":[14,111,166,197,236,273,313,348],"<mml:mi>j</mml:mi>":[15,169,200],"<mml:mo":[16,21,113,118,170,175,201,207,238,243,277,280,317,326],"stretchy=\"false\">(</mml:mo>":[17,114,171,202,239,278,318],"<mml:mi>":[18,172,204],"\u03c4":[19,173,205],"</mml:mi>":[20,55,148,174,206],"stretchy=\"false\">)</mml:mo>":[22,119,176,208,244,281,327],"</mml:mrow>":[23,122,177,209,245,289,291,324,328],"<mml:annotation":[24,56,74,90,123,149,178,210,246,292,329],"encoding=\"application/x-tex\">j(\\tau":[25],")</mml:annotation>":[26,180,212],"</mml:semantics>":[27,58,76,92,125,151,181,213,248,295,331],"</mml:math>":[28,59,77,93,126,152,182,214,249,296,332],"</inline-formula>":[29,60,78,94,127,153,183,215,250,297,333],"and":[30,184],"its":[31,38],"modular":[32],"equations":[33],"with":[34,128],"no":[35],"perception":[36],"of":[37,222,224],"related":[39],"classical":[40],"group":[41],"structure":[42],"except":[43],"at":[44,137],"alttext=\"normal":[49,142],"infinity\">":[50,143],"<mml:mi":[52,145],"mathvariant=\"normal\">":[53,146],"\u221e":[54,147],"encoding=\"application/x-tex\">\\infty</mml:annotation>":[57,150],".":[61],"We":[62,217],"start":[63],"by":[64],"taking,":[65],"for":[66,154],"alttext=\"p\">":[71,87],"<mml:mi>p</mml:mi>":[73,89,203,323],"encoding=\"application/x-tex\">p</mml:annotation>":[75,91],"prime,":[79],"an":[80],"unknown":[81],"\u201c":[82],"-Newtonian\u201d":[95],"polynomial":[96],"equation":[97],"alttext=\"g":[102,229],"u":[104,231,264,305],"comma":[105,232],"v":[106,233],"right-parenthesis":[107,267],"equals":[108,160,190,263,304,340],"0\">":[109],"<mml:mi>g</mml:mi>":[112,237],"<mml:mi>u</mml:mi>":[115,167,240,274,276,316],"<mml:mo>,</mml:mo>":[116,241],"<mml:mi>v</mml:mi>":[117,198,242,314],"<mml:mo>=</mml:mo>":[120,168,199,275,315,350],"<mml:mn>0</mml:mn>":[121],"encoding=\"application/x-tex\">g(u,v)=0</mml:annotation>":[124],"arbitrary":[129],"coefficients":[130,223],"(based":[131],"only":[132],"on":[133],"Newton\u2019s":[134],"polygon":[135],"requirements":[136],"alttext=\"u":[159,262],"j":[161,191],"encoding=\"application/x-tex\">u=j(\\tau":[179],"alttext=\"v":[189,303],"p":[193,309],"encoding=\"application/x-tex\">v=j(p\\tau":[211],").":[216],"then":[218],"ask":[219],"which":[220],"choice":[221],"encoding=\"application/x-tex\">g(u,v)</mml:annotation>":[247],"leads":[251],"some":[253],"consistent":[254],"Laurent":[255],"series":[256],"solution":[257],"q":[266,307],"almost-equals":[268],"1":[269],"slash":[270],"q\">":[271],"<mml:mi>q</mml:mi>":[279,290,320,349],"<mml:mo>":[282],"\u2248":[283],"</mml:mo>":[284],"<mml:mn>1</mml:mn>":[285],"<mml:mrow":[286,321],"class=\"MJX-TeXAtom-ORD\">":[287,322],"<mml:mo>/</mml:mo>":[288],"encoding=\"application/x-tex\">u=u(q)\\approx":[293],"1/q</mml:annotation>":[294],",":[298],"Superscript":[308],"Baseline":[310],"<mml:msup>":[319],"</mml:msup>":[325],"encoding=\"application/x-tex\">v=u(q^{p})</mml:annotation>":[330],"(where":[334],"alttext=\"q":[339],"exp":[341],"2":[342],"pi":[343],"i":[344],"<mml:mi>exp</mml:mi>":[351]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}