{"id":"https://openalex.org/W2181048585","doi":"https://doi.org/10.1112/s1461157016000140","title":"A census of zeta functions of quartic K surfaces over","display_name":"A census of zeta functions of quartic K surfaces over","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2181048585","doi":"https://doi.org/10.1112/s1461157016000140","mag":"2181048585"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157016000140","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157016000140","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/514C89A1FE39BEE2565518DA51DB3B5C/S1461157016000140a.pdf/div-class-title-a-census-of-zeta-functions-of-quartic-k-span-class-inlineformula-span-class-alternatives-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-gif-data-type-simple-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20160907143622272-0774-s1461157016000140-inline1-gif-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-3-span-span-span-span-surfaces-over-span-class-inlineformula-span-class-alternatives-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-gif-data-type-simple-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20160907143622272-0774-s1461157016000140-inline2-gif-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-mathbb-f-2-span-span-span-span-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/514C89A1FE39BEE2565518DA51DB3B5C/S1461157016000140a.pdf/div-class-title-a-census-of-zeta-functions-of-quartic-k-span-class-inlineformula-span-class-alternatives-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-gif-data-type-simple-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20160907143622272-0774-s1461157016000140-inline1-gif-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-3-span-span-span-span-surfaces-over-span-class-inlineformula-span-class-alternatives-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-gif-data-type-simple-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20160907143622272-0774-s1461157016000140-inline2-gif-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-mathbb-f-2-span-span-span-span-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036080574","display_name":"Kiran S. Kedlaya","orcid":"https://orcid.org/0000-0001-8700-8758"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kiran S. Kedlaya","raw_affiliation_strings":["Department of Mathematics, University of California, San Diego, 9500 Gilman Drive #0112, La Jolla, CA\u00a092093, USA email","Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139 United States of America","Department of Mathematics University of California, San Diego 9500 Gilman Drive #0112 La Jolla, CA 92093 United States of America"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, 9500 Gilman Drive #0112, La Jolla, CA\u00a092093, USA email","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139 United States of America","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Mathematics University of California, San Diego 9500 Gilman Drive #0112 La Jolla, CA 92093 United States of America","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005412948","display_name":"Andrew V. Sutherland","orcid":"https://orcid.org/0000-0001-7739-2792"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew V. Sutherland","raw_affiliation_strings":["Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA\u00a002139, USA email","Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139 United States of America","Department of Mathematics University of California, San Diego 9500 Gilman Drive #0112 La Jolla, CA 92093 United States of America"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA\u00a002139, USA email","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139 United States of America","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Mathematics University of California, San Diego 9500 Gilman Drive #0112 La Jolla, CA 92093 United States of America","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036080574"],"corresponding_institution_ids":["https://openalex.org/I36258959","https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.02956155,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"19","issue":"A","first_page":"1","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9988999962806702,"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":0.9782999753952026,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8642387390136719},{"id":"https://openalex.org/keywords/quartic-function","display_name":"Quartic function","score":0.7852283716201782},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5632559657096863},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.48684853315353394},{"id":"https://openalex.org/keywords/transcendental-number","display_name":"Transcendental number","score":0.46700963377952576},{"id":"https://openalex.org/keywords/arithmetic-zeta-function","display_name":"Arithmetic zeta function","score":0.4539794623851776},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.45206886529922485},{"id":"https://openalex.org/keywords/transcendental-function","display_name":"Transcendental function","score":0.4421337842941284},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4396376311779022},{"id":"https://openalex.org/keywords/prime-zeta-function","display_name":"Prime zeta function","score":0.43056583404541016},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4264809191226959},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42152833938598633},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35692286491394043},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32421010732650757}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8642387390136719},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.7852283716201782},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5632559657096863},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.48684853315353394},{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.46700963377952576},{"id":"https://openalex.org/C35861355","wikidata":"https://www.wikidata.org/wiki/Q4791135","display_name":"Arithmetic zeta function","level":3,"score":0.4539794623851776},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.45206886529922485},{"id":"https://openalex.org/C43321923","wikidata":"https://www.wikidata.org/wiki/Q864333","display_name":"Transcendental function","level":2,"score":0.4421337842941284},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4396376311779022},{"id":"https://openalex.org/C71897612","wikidata":"https://www.wikidata.org/wiki/Q1896470","display_name":"Prime zeta function","level":4,"score":0.43056583404541016},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4264809191226959},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42152833938598633},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35692286491394043},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32421010732650757},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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":[{"id":"doi:10.1112/s1461157016000140","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157016000140","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/514C89A1FE39BEE2565518DA51DB3B5C/S1461157016000140a.pdf/div-class-title-a-census-of-zeta-functions-of-quartic-k-span-class-inlineformula-span-class-alternatives-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-gif-data-type-simple-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20160907143622272-0774-s1461157016000140-inline1-gif-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-3-span-span-span-span-surfaces-over-span-class-inlineformula-span-class-alternatives-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-gif-data-type-simple-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20160907143622272-0774-s1461157016000140-inline2-gif-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-mathbb-f-2-span-span-span-span-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1511.06945","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.06945","pdf_url":"https://arxiv.org/pdf/1511.06945","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"}],"best_oa_location":{"id":"doi:10.1112/s1461157016000140","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157016000140","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/514C89A1FE39BEE2565518DA51DB3B5C/S1461157016000140a.pdf/div-class-title-a-census-of-zeta-functions-of-quartic-k-span-class-inlineformula-span-class-alternatives-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-gif-data-type-simple-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20160907143622272-0774-s1461157016000140-inline1-gif-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-3-span-span-span-span-surfaces-over-span-class-inlineformula-span-class-alternatives-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-gif-data-type-simple-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20160907143622272-0774-s1461157016000140-inline2-gif-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-mathbb-f-2-span-span-span-span-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4000000059604645,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G2403635342","display_name":"Computational Methods in Arithmetic Geometry","funder_award_id":"1522526","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2528972923","display_name":"Computational methods in arithmetic geometry","funder_award_id":"1115455","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5379992368","display_name":"Applications and extensions of p-adic Hodge theory","funder_award_id":"1501214","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332603","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2181048585.pdf","grobid_xml":"https://content.openalex.org/works/W2181048585.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W605964321","https://openalex.org/W1484607325","https://openalex.org/W1496801598","https://openalex.org/W1497727960","https://openalex.org/W1520628662","https://openalex.org/W1545876477","https://openalex.org/W1571913868","https://openalex.org/W1574151794","https://openalex.org/W1597260315","https://openalex.org/W1599036550","https://openalex.org/W1669872106","https://openalex.org/W1966938553","https://openalex.org/W2026258986","https://openalex.org/W2031076937","https://openalex.org/W2034694871","https://openalex.org/W2076178640","https://openalex.org/W2113600343","https://openalex.org/W2125335450","https://openalex.org/W2165086961","https://openalex.org/W2290361708","https://openalex.org/W2462509349","https://openalex.org/W2531879069","https://openalex.org/W2606122765","https://openalex.org/W2780608926","https://openalex.org/W2963245729","https://openalex.org/W2963686199","https://openalex.org/W3099733697","https://openalex.org/W3106399383","https://openalex.org/W4249240057","https://openalex.org/W4252526275","https://openalex.org/W4255213956"],"related_works":["https://openalex.org/W68100126","https://openalex.org/W2962759484","https://openalex.org/W3104284816","https://openalex.org/W2118298494","https://openalex.org/W4301816606","https://openalex.org/W3004861521","https://openalex.org/W1538695297","https://openalex.org/W2063818956","https://openalex.org/W2092735642","https://openalex.org/W2963124686"],"abstract_inverted_index":{"We":[0],"compute":[1],"the":[2,8,20,28],"complete":[3,29],"set":[4,30],"of":[5,11,31,34,66,78],"candidates":[6],"for":[7,62],"zeta":[9,32,64],"function":[10],"a":[12,59,71,75],"K":[13,67],"$3$":[14,68],"surface":[15],"over":[16,38],"$\\mathbb{F}_{2}$":[17,39],"consistent":[18],"with":[19],"Weil":[21],"and":[22],"Tate":[23],"conjectures,":[24],"as":[25,27],"well":[26],"functions":[33,65],"smooth":[35],"quartic":[36],"surfaces":[37],".":[40],"These":[41],"sets":[42],"differ":[43],"substantially,":[44],"but":[45],"we":[46],"do":[47],"identify":[48],"natural":[49],"subsets":[50],"which":[51,81],"coincide.":[52],"This":[53],"gives":[54],"some":[55],"numerical":[56],"evidence":[57],"towards":[58],"Honda\u2013Tate":[60],"theorem":[61,77],"transcendental":[63],"surfaces;":[69],"such":[70],"result":[72],"would":[73],"refine":[74],"recent":[76],"Taelman,":[79],"in":[80],"one":[82],"must":[83],"allow":[84],"an":[85],"uncontrolled":[86],"base":[87],"field":[88],"extension.":[89]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2016-06-24T00:00:00"}