{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:38:08Z","timestamp":1776728288828,"version":"3.51.2"},"reference-count":5,"publisher":"American Mathematical Society (AMS)","issue":"238","license":[{"start":{"date-parts":[[2002,9,17]],"date-time":"2002-09-17T00:00:00Z","timestamp":1032220800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We determine the explicit form of the Igusa local zeta function associated to an elliptic curve. The denominator is known to be trivial. Here we determine the possible numerators and classify them according to the Kodaira\u2013N\u00e9ron classification of the special fibers of elliptic curves as determined by Tate\u2019s algorithm.<\/p>","DOI":"10.1090\/s0025-5718-01-01396-5","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"815-823","source":"Crossref","is-referenced-by-count":1,"title":["The Igusa local zeta functions of elliptic curves"],"prefix":"10.1090","volume":"71","author":[{"given":"Diane","family":"Meuser","sequence":"first","affiliation":[]},{"given":"Margaret","family":"Robinson","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2001,9,17]]},"reference":[{"key":"1","isbn-type":"print","first-page":"175","article-title":"A stationary phase formula for \ud835\udc5d-adic integrals and its applications","author":"Igusa, Jun-ichi","year":"1994","ISBN":"https:\/\/id.crossref.org\/isbn\/0387941762"},{"issue":"3","key":"2","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1007\/BF01388439","article-title":"On the poles of a local zeta function for curves","volume":"73","author":"Meuser, D.","year":"1983","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"key":"3","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0851-8","volume-title":"Advanced topics in the arithmetic of elliptic curves","volume":"151","author":"Silverman, Joseph H.","year":"1994","ISBN":"https:\/\/id.crossref.org\/isbn\/0387943285"},{"key":"4","first-page":"33","article-title":"Algorithm for determining the type of a singular fiber in an elliptic pencil","author":"Tate, J.","year":"1975"},{"issue":"1","key":"5","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1112\/jlms\/s2-41.1.27","article-title":"On the poles of Igusa\u2019s local zeta function for curves","volume":"41","author":"Veys, W.","year":"1990","journal-title":"J. London Math. Soc. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6107","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01396-5\/S0025-5718-01-01396-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01396-5\/S0025-5718-01-01396-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:56:53Z","timestamp":1776725813000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01396-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,9,17]]},"references-count":5,"journal-issue":{"issue":"238","published-print":{"date-parts":[[2002,4]]}},"alternative-id":["S0025-5718-01-01396-5"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-01-01396-5","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2001,9,17]]}}}