{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:43:10Z","timestamp":1776789790867,"version":"3.51.2"},"reference-count":19,"publisher":"American Mathematical Society (AMS)","issue":"266","license":[{"start":{"date-parts":[[2009,8,22]],"date-time":"2009-08-22T00:00:00Z","timestamp":1250899200000},"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>\n                    Constructing number fields with prescribed ramification is an important problem in computational number theory. In this paper, we consider the problem of computing all imprimitive number fields of a given degree which are unramified outside of a given finite set of primes\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S\">\n                        <mml:semantics>\n                          <mml:mi>S<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">S<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    by combining the techniques of targeted Hunter searches with Martinet\u2019s relative version of Hunter\u2019s theorem. We then carry out this algorithm to generate complete tables of imprimitive number fields for degrees\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"4\">\n                        <mml:semantics>\n                          <mml:mn>4<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">4<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    through\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"10\">\n                        <mml:semantics>\n                          <mml:mn>10<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">10<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and certain sets\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S\">\n                        <mml:semantics>\n                          <mml:mi>S<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">S<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of small primes.\n                  <\/p>","DOI":"10.1090\/s0025-5718-08-02178-9","type":"journal-article","created":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T13:09:23Z","timestamp":1259672963000},"page":"1109-1117","source":"Crossref","is-referenced-by-count":4,"title":["A targeted Martinet search"],"prefix":"10.1090","volume":"78","author":[{"given":"Eric","family":"Driver","sequence":"first","affiliation":[]},{"given":"John","family":"Jones","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2008,8,22]]},"reference":[{"key":"1","unstructured":"BOINC, Berkeley Open Infrastructure for Network Computing. \\url{http:\/\/boinc.berkeley.edu}"},{"key":"2","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"},{"key":"3","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8489-0","volume-title":"Advanced topics in computational number theory","volume":"193","author":"Cohen, Henri","year":"2000","ISBN":"https:\/\/id.crossref.org\/isbn\/0387987274"},{"issue":"1","key":"4","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/0022-314X(87)90014-X","article-title":"Petits discriminants des corps de nombres totalement imaginaires de degr\u00e9 8","volume":"25","author":"Diaz y Diaz, F.","year":"1987","journal-title":"J. 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Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"6","isbn-type":"print","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1090\/crmp\/019\/16","article-title":"Sextic number fields with discriminant (-1)^{\ud835\udc57}2^{\ud835\udc4e}3^{\ud835\udc4f}","author":"Jones, John W.","year":"1999","ISBN":"https:\/\/id.crossref.org\/isbn\/0821809644"},{"issue":"244","key":"7","doi-asserted-by":"publisher","first-page":"1975","DOI":"10.1090\/S0025-5718-03-01510-2","article-title":"Septic fields with discriminant \u00b12^{\ud835\udc4e}3^{\ud835\udc4f}","volume":"72","author":"Jones, John W.","year":"2003","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"8","unstructured":"J. Jones, Tables of number fields with prescribed ramification, \\url{http:\/\/math.la.asu.edu\/ jj\/numberfields}"},{"key":"9","unstructured":"E. Driver, Tables of number fields with prescribed ramification, \\url{http:\/\/hobbes.la.asu.edu\/Number_{F}ields\/Driver\/FieldTables.html}"},{"key":"10","unstructured":"E. Driver, A Targeted Martinet Search, Ph.D. Thesis, Arizona State University, December 2006."},{"issue":"255","key":"11","doi-asserted-by":"publisher","first-page":"1519","DOI":"10.1090\/S0025-5718-06-01827-8","article-title":"The nonexistence of nonsolvable octic number fields ramified only at one small prime","volume":"75","author":"Sylla, Lesseni","year":"2006","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"3","key":"12","doi-asserted-by":"publisher","first-page":"617","DOI":"10.5802\/jtnb.562","article-title":"Nonsolvable nonic number fields ramified only at one small prime","volume":"18","author":"Lesseni, Sylla","year":"2006","journal-title":"J. Th\\'{e}or. Nombres Bordeaux","ISSN":"https:\/\/id.crossref.org\/issn\/1246-7405","issn-type":"print"},{"key":"13","isbn-type":"print","first-page":"147","article-title":"Methodes g\u00e9om\u00e9triques dans la recherche des petits discriminants","author":"Martinet, Jacques","year":"1985","ISBN":"https:\/\/id.crossref.org\/isbn\/0817633154"},{"key":"14","unstructured":"PARI2, 2000. PARI\/GP, Version 2.1.4. The PARI Group, Bordeaux. \\url{http:\/\/www.parigp-home.de}"},{"issue":"1","key":"15","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/0022-314X(82)90061-0","article-title":"On the computation of number fields of small discriminants including the minimum discriminants of sixth degree fields","volume":"14","author":"Pohst, Michael","year":"1982","journal-title":"J. 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