{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:38:18Z","timestamp":1776800298623,"version":"3.51.2"},"reference-count":36,"publisher":"American Mathematical Society (AMS)","issue":"300","license":[{"start":{"date-parts":[[2016,11,3]],"date-time":"2016-11-03T00:00:00Z","timestamp":1478131200000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100000146","name":"Alberta Innovates - Technology Futures","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000146","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n We present an improved algorithm for tabulating class groups of imaginary quadratic fields of bounded discriminant. Our method uses classical class number formulas involving theta-series to compute the group orders unconditionally for all\n \n \n \n \n \n \u0394\n \n <\/mml:mi>\n \u2262<\/mml:mo>\n 1<\/mml:mn>\n \n (<\/mml:mo>\n mod<\/mml:mi>\n \n 8<\/mml:mn>\n )<\/mml:mo>\n .<\/mml:mo>\n <\/mml:mrow>\n \\Delta \\not \\equiv 1 \\pmod {8}.<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n The group structure is resolved using the factorization of the group order. The\n \n \n \n \n 1<\/mml:mn>\n mod<\/mml:mo>\n 8<\/mml:mn>\n <\/mml:mrow>\n 1 \\bmod 8<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n case was handled using the methods of Jacobson, Ramachandran, and Williams including the batch verification method based on the Eichler-Selberg trace formula to remove dependence on the Extended Riemann Hypothesis. Our new method enabled us to extend the previous bound of\n \n \n \n \n \n |<\/mml:mo>\n <\/mml:mrow>\n \n \u0394\n \n <\/mml:mi>\n \n |<\/mml:mo>\n <\/mml:mrow>\n ><\/mml:mo>\n 2<\/mml:mn>\n \n \u22c5\n \n <\/mml:mo>\n \n 10<\/mml:mn>\n \n 11<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n |\\Delta | > 2 \\cdot 10^{11}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n to\n \n \n \n \n 2<\/mml:mn>\n \n 40<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n 2^{40}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n . Statistical data in support of a variety of conjectures is presented, along with new examples of class groups with exotic structures.\n <\/p>","DOI":"10.1090\/mcom3050","type":"journal-article","created":{"date-parts":[[2015,3,4]],"date-time":"2015-03-04T10:56:36Z","timestamp":1425466596000},"page":"1983-2009","source":"Crossref","is-referenced-by-count":8,"title":["Unconditional class group tabulation of imaginary quadratic fields to |\u0394|<2\u2074\u2070"],"prefix":"10.1090","volume":"85","author":[{"given":"A.","family":"Mosunov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jr.","family":"M. J. 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