{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:41:42Z","timestamp":1776724902407,"version":"3.51.2"},"reference-count":37,"publisher":"American Mathematical Society (AMS)","issue":"228","license":[{"start":{"date-parts":[[2000,5,24]],"date-time":"2000-05-24T00:00:00Z","timestamp":959126400000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper we compute the relative class number of all imaginary Abelian fields of prime conductor below 10000. Our approach is based on a novel multiple evaluation technique, and, assuming the ERH, it has a running time of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper O left-parenthesis p squared log squared left-parenthesis p right-parenthesis log log left-parenthesis p right-parenthesis right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>O<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>p<\/mml:mi>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:msup>\n                              <mml:mi>log<\/mml:mi>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>\n                              \u2061\n                              \n                            <\/mml:mo>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mi>log<\/mml:mi>\n                            <mml:mo>\n                              \u2061\n                              \n                            <\/mml:mo>\n                            <mml:mi>log<\/mml:mi>\n                            <mml:mo>\n                              \u2061\n                              \n                            <\/mml:mo>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">O(p^2\\log ^2(p)\\log \\log (p))<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , where\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is the conductor of the field.\n                  <\/p>","DOI":"10.1090\/s0025-5718-99-01139-4","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:13:53Z","timestamp":1027707233000},"page":"1717-1728","source":"Crossref","is-referenced-by-count":3,"title":["Relative class number of imaginary Abelian fields of prime conductor below 10000"],"prefix":"10.1090","volume":"68","author":[{"given":"M.","family":"Shokrollahi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[1999,5,24]]},"reference":[{"key":"1","unstructured":"C. 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