{"id":"https://openalex.org/W2025611151","doi":"https://doi.org/10.1090/s0025-5718-99-01051-0","title":"Calculation of values of \ud835\udc3f-functions associated to elliptic curves","display_name":"Calculation of values of \ud835\udc3f-functions associated to elliptic curves","publication_year":1999,"publication_date":"1999-02-10","ids":{"openalex":"https://openalex.org/W2025611151","doi":"https://doi.org/10.1090/s0025-5718-99-01051-0","mag":"2025611151"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-99-01051-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01051-0","pdf_url":"https://www.ams.org/mcom/1999-68-227/S0025-5718-99-01051-0/S0025-5718-99-01051-0.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/1999-68-227/S0025-5718-99-01051-0/S0025-5718-99-01051-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067137356","display_name":"Shigeki Akiyama","orcid":"https://orcid.org/0000-0001-7549-6686"},"institutions":[{"id":"https://openalex.org/I71395657","display_name":"Niigata University","ror":"https://ror.org/04ww21r56","country_code":"JP","type":"education","lineage":["https://openalex.org/I71395657"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Shigeki Akiyama","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Niigata University, Ikarashi 2-8050, Niigata 950-2181, Japan","Department of Mathematics, Faculty of Science Niigata University, Ikarashi 2-8050, Niigata 950-2181, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Niigata University, Ikarashi 2-8050, Niigata 950-2181, Japan","institution_ids":["https://openalex.org/I71395657"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science Niigata University, Ikarashi 2-8050, Niigata 950-2181, Japan","institution_ids":["https://openalex.org/I71395657"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049795616","display_name":"Yoshio Tanigawa","orcid":"https://orcid.org/0000-0002-4308-4481"},"institutions":[{"id":"https://openalex.org/I60134161","display_name":"Nagoya University","ror":"https://ror.org/04chrp450","country_code":"JP","type":"education","lineage":["https://openalex.org/I60134161"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yoshio Tanigawa","raw_affiliation_strings":["Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan","Graduate School of Mathematics , Nagoya University , Chikusa-ku , Nagoya 464-8602 , Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan","institution_ids":["https://openalex.org/I60134161"]},{"raw_affiliation_string":"Graduate School of Mathematics , Nagoya University , Chikusa-ku , Nagoya 464-8602 , Japan","institution_ids":["https://openalex.org/I60134161"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5067137356"],"corresponding_institution_ids":["https://openalex.org/I71395657"],"apc_list":null,"apc_paid":null,"fwci":1.4414,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.78492206,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"68","issue":"227","first_page":"1201","last_page":"1231"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9973000288009644,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/algorithm","display_name":"Algorithm","score":0.6329960227012634},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.4316667914390564},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4118833839893341},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40469467639923096},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3298071026802063}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6329960227012634},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.4316667914390564},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4118833839893341},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40469467639923096},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3298071026802063}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-99-01051-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01051-0","pdf_url":"https://www.ams.org/mcom/1999-68-227/S0025-5718-99-01051-0/S0025-5718-99-01051-0.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:CiteSeerX.psu:10.1.1.364.1413","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.364.1413","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/journals/mcom/1999-68-227/S0025-5718-99-01051-0/S0025-5718-99-01051-0.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-99-01051-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01051-0","pdf_url":"https://www.ams.org/mcom/1999-68-227/S0025-5718-99-01051-0/S0025-5718-99-01051-0.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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2025611151.pdf","grobid_xml":"https://content.openalex.org/works/W2025611151.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W347294826","https://openalex.org/W1504035215","https://openalex.org/W1529471319","https://openalex.org/W1538733621","https://openalex.org/W1607458528","https://openalex.org/W1967258857","https://openalex.org/W1995040226","https://openalex.org/W1998428445","https://openalex.org/W2002596763","https://openalex.org/W2010436631","https://openalex.org/W2016499826","https://openalex.org/W2042837137","https://openalex.org/W2043708719","https://openalex.org/W2072247311","https://openalex.org/W2093171821","https://openalex.org/W2094232328","https://openalex.org/W2106226212","https://openalex.org/W2117060314","https://openalex.org/W2329964106","https://openalex.org/W2333976070","https://openalex.org/W2607541626","https://openalex.org/W4285719527","https://openalex.org/W4302394292","https://openalex.org/W6651045016"],"related_works":["https://openalex.org/W2748952813","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/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552"],"abstract_inverted_index":{"We":[0,63],"calculated":[1],"numerically":[2],"the":[3,26,30,67,75,109,139,148,159,233],"values":[4],"of":[5,20],"<inline-formula":[6,32,78,112,163,198],"content-type=\"math/mathml\">":[7,33,79,113,164,199],"<mml:math":[8,34,80,114,165,200],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[9,35,81,115,166,201],"alttext=\"upper":[10],"L\">":[11],"<mml:semantics>":[12,42,88,119,173,206],"<mml:mi>L</mml:mi>":[13],"<mml:annotation":[14,55,99,125,184,215],"encoding=\"application/x-tex\">L</mml:annotation>":[15],"</mml:semantics>":[16,59,102,127,187,218],"</mml:math>":[17,60,103,128,188,219],"</inline-formula>":[18,61,104,129,189,220],"-functions":[19],"four":[21],"typical":[22],"elliptic":[23],"curves":[24],"in":[25,29,70,135,147],"critical":[27,76],"strip":[28],"range":[31,72],"alttext=\"Im":[36,202],"left-parenthesis":[37,83,168,203],"s":[38,84,169,204],"right-parenthesis":[39,85,170],"less-than-or-equal-to":[40],"400\">":[41],"<mml:mrow>":[43,89,120,174,207],"<mml:mtext>Im</mml:mtext>":[44,208],"<mml:mo":[45,48,91,94,176,179,209,212],"stretchy=\"false\">(</mml:mo>":[46,92,177,210],"<mml:mi>s</mml:mi>":[47,93,121,178,211],"stretchy=\"false\">)</mml:mo>":[49,95,180,213],"<mml:mo>":[50],"\u2264":[51],"</mml:mo>":[52],"<mml:mn>400</mml:mn>":[53],"</mml:mrow>":[54,98,124,183,214],"encoding=\"application/x-tex\">\\text":[56,100,185,216],"{Im}(s)\\leq":[57],"400</mml:annotation>":[58],".":[62,130,221],"found":[64],"that":[65,225],"all":[66],"non-trivial":[68],"zeros":[69],"this":[71,136],"lie":[73],"on":[74],"line":[77],"alttext=\"Re":[82,167],"equals":[86,117],"1\">":[87,118],"<mml:mtext>Re</mml:mtext>":[90,175],"<mml:mo>=</mml:mo>":[96,122],"<mml:mn>1</mml:mn>":[97,123],"{Re}(s)=1</mml:annotation>":[101],"and":[105,232],"are":[106],"simple":[107],"except":[108],"one":[110],"at":[111],"alttext=\"s":[116],"encoding=\"application/x-tex\">s=1</mml:annotation>":[126],"The":[131],"method":[132],"we":[133,154,223],"employed":[134],"paper":[137],"is":[138],"approximate":[140],"functional":[141],"equation":[142],"with":[143],"incomplete":[144,151],"gamma":[145,152],"functions":[146],"coefficients.":[149],"For":[150],"functions,":[153],"continued":[155],"them":[156],"holomorphically":[157],"to":[158,194],"right":[160],"half":[161],"plane":[162],"greater-than":[171],"0\">":[172],"<mml:mo>&gt;</mml:mo>":[181],"<mml:mn>0</mml:mn>":[182],"{Re}(s)&gt;0</mml:annotation>":[186],",":[190],"which":[191],"enables":[192],"us":[193],"calculate":[195],"for":[196],"large":[197],"right-parenthesis\">":[205],"{Im}(s)</mml:annotation>":[217],"Furthermore":[222],"remark":[224],"a":[226],"relation":[227],"exists":[228],"between":[229],"Sato-Tate":[230],"conjecture":[231],"generalized":[234],"Riemann":[235],"Hypothesis.":[236]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
