{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T11:02:30Z","timestamp":1776769350658,"version":"3.51.2"},"reference-count":18,"publisher":"American Mathematical Society (AMS)","issue":"222","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n We use the algorithmic computation of exact sequences of Abelian groups to compute the complete structure of\n \n \n \n \n (<\/mml:mo>\n \n \n Z<\/mml:mi>\n <\/mml:mrow>\n \n K<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n \n \/<\/mml:mo>\n <\/mml:mrow>\n \n m<\/mml:mi>\n <\/mml:mrow>\n \n )<\/mml:mo>\n \n \n \u2217\n \n <\/mml:mo>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n (\\mathbb {Z}_{K}\/\\mathfrak {m})^{*}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n for an ideal\n \n \n \n \n m<\/mml:mi>\n <\/mml:mrow>\n \\mathfrak {m}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n of a number field\n \n \n \n K<\/mml:mi>\n K<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n , as well as ray class groups of number fields, and conductors and discriminants of the corresponding Abelian extensions. As an application we give several number fields with discriminants less than previously known ones.\n <\/p>","DOI":"10.1090\/s0025-5718-98-00912-0","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"773-795","source":"Crossref","is-referenced-by-count":22,"title":["Computing ray class groups, conductors and discriminants"],"prefix":"10.1090","volume":"67","author":[{"given":"H.","family":"Cohen","sequence":"first","affiliation":[]},{"given":"F.","family":"y Diaz","sequence":"additional","affiliation":[]},{"given":"M.","family":"Olivier","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1006\/jagm.1993.1038","article-title":"Factor refinement","volume":"15","author":"Bach, Eric","year":"1993","journal-title":"J. Algorithms","ISSN":"https:\/\/id.crossref.org\/issn\/0196-6774","issn-type":"print"},{"key":"2","volume-title":"Algebraic number theory","year":"1967"},{"key":"3","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02945-9","volume-title":"A course in computational algebraic number theory","volume":"138","author":"Cohen, Henri","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/3540556400"},{"issue":"216","key":"4","doi-asserted-by":"publisher","first-page":"1681","DOI":"10.1090\/S0025-5718-96-00766-1","article-title":"Hermite and Smith normal form algorithms over Dedekind domains","volume":"65","author":"Cohen, Henri","year":"1996","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"2","key":"5","doi-asserted-by":"crossref","first-page":"351","DOI":"10.5802\/jtnb.55","article-title":"A polynomial reduction algorithm","volume":"3","author":"Cohen, Henri","year":"1991","journal-title":"S\\'{e}m. Th\\'{e}or. Nombres Bordeaux (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0989-5558","issn-type":"print"},{"key":"6","unstructured":"[Co-Di-Ol] H. Cohen, F. Diaz y Diaz and M. Olivier, Algorithmic methods for finitely generated Abelian groups, submitted to J. of Symbolic Computation 1996."},{"key":"7","doi-asserted-by":"crossref","unstructured":"[Da-Po] M. Daberkow and M. Pohst, Computations with relative extensions of number fields with an application to the construction of Hilbert class fields, Proc. ISAAC\u201995 (1995) (to appear).","DOI":"10.1145\/220346.220355"},{"key":"8","unstructured":"[Di-Ol] F. Diaz y Diaz and M. Olivier, Algorithmique Alg\u00e9brique dans les Corps de Nombres, Etat de la Recherche en Algorithmique Arithm\u00e9tique, Laboratoire A2X, Bordeaux, 1995."},{"key":"9","first-page":"87","article-title":"Hermite normal form computation for integer matrices","volume":"105","author":"Havas, George","year":"1994","journal-title":"Congr. Numer.","ISSN":"https:\/\/id.crossref.org\/issn\/0384-9864","issn-type":"print"},{"key":"10","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4092-9","volume-title":"Lectures on the theory of algebraic numbers","volume":"77","author":"Hecke, Erich","year":"1981","ISBN":"https:\/\/id.crossref.org\/isbn\/0387905952"},{"issue":"2","key":"11","doi-asserted-by":"publisher","first-page":"83","DOI":"10.5802\/aif.1011","article-title":"Euclidean fields having a large Lenstra constant","volume":"35","author":"Leutbecher, Armin","year":"1985","journal-title":"Ann. Inst. Fourier (Grenoble)","ISSN":"https:\/\/id.crossref.org\/issn\/0373-0956","issn-type":"print"},{"key":"12","isbn-type":"print","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1007\/BFb0086551","article-title":"On cliques of exceptional units and Lenstra\u2019s construction of Euclidean fields","author":"Leutbecher, Armin","year":"1989","ISBN":"https:\/\/id.crossref.org\/isbn\/0387513973"},{"key":"13","isbn-type":"print","first-page":"151","article-title":"Petits discriminants des corps de nombres","author":"Martinet, Jacques","year":"1982","ISBN":"https:\/\/id.crossref.org\/isbn\/0521285135"},{"key":"14","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1017\/S0027763000018316","article-title":"The structure of the multiplicative group of residue classes modulo \ud835\udd2d^{\ud835\udd11+1}","volume":"73","author":"Nakagoshi, Norikata","year":"1979","journal-title":"Nagoya Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0027-7630","issn-type":"print"},{"issue":"1","key":"15","doi-asserted-by":"crossref","first-page":"119","DOI":"10.5802\/jtnb.22","article-title":"Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions: a survey of recent results","volume":"2","author":"Odlyzko, A. M.","year":"1990","journal-title":"S\\'{e}m. Th\\'{e}or. Nombres Bordeaux (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0989-5558","issn-type":"print"},{"key":"16","series-title":"Encyclopedia of Mathematics and its Applications","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511661952","volume-title":"Algorithmic algebraic number theory","volume":"30","author":"Pohst, M.","year":"1989","ISBN":"https:\/\/id.crossref.org\/isbn\/0521330602"},{"key":"17","unstructured":"[Rob] X.-F. Roblot, Unit\u00e9s de Stark et corps de classes de Hilbert, C. R. Acad. Sci. Paris 323 (1996), 1165\u20131168."},{"key":"18","isbn-type":"print","first-page":"213","article-title":"Class numbers and units","author":"Zantema, H.","year":"1982","ISBN":"https:\/\/id.crossref.org\/isbn\/9061962498"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1998-67-222\/S0025-5718-98-00912-0\/S0025-5718-98-00912-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1998-67-222\/S0025-5718-98-00912-0\/S0025-5718-98-00912-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:45:10Z","timestamp":1776721510000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1998-67-222\/S0025-5718-98-00912-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998]]},"references-count":18,"journal-issue":{"issue":"222","published-print":{"date-parts":[[1998,4]]}},"alternative-id":["S0025-5718-98-00912-0"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-98-00912-0","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":[[1998]]}}}