{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:44:31Z","timestamp":1776833071492,"version":"3.51.2"},"reference-count":30,"publisher":"American Mathematical Society (AMS)","issue":"254","license":[{"start":{"date-parts":[[2006,11,29]],"date-time":"2006-11-29T00:00:00Z","timestamp":1164758400000},"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                    We will show that the normal CM-fields with relative class number one are of degrees\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"less-than-or-equal-to 216\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mn>216<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\leq 216<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Moreover, if we assume the Generalized Riemann Hypothesis, then the normal CM-fields with relative class number one are of degrees\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"less-than-or-equal-to 96\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mn>96<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\leq 96<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , and the CM-fields with class number one are of degrees\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"less-than-or-equal-to 104\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mn>104<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\leq 104<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . By many authors all normal CM-fields of degrees\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"less-than-or-equal-to 96\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mn>96<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\leq 96<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with class number one are known except for the possible fields of degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"64\">\n                        <mml:semantics>\n                          <mml:mn>64<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">64<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    or\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"96\">\n                        <mml:semantics>\n                          <mml:mn>96<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">96<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Consequently the class number one problem for normal CM-fields is solved under the Generalized Riemann Hypothesis except for these two cases.\n                  <\/p>","DOI":"10.1090\/s0025-5718-05-01811-9","type":"journal-article","created":{"date-parts":[[2006,2,15]],"date-time":"2006-02-15T11:05:20Z","timestamp":1140001520000},"page":"997-1013","source":"Crossref","is-referenced-by-count":6,"title":["CM-fields with relative class number one"],"prefix":"10.1090","volume":"75","author":[{"given":"Geon-No","family":"Lee","sequence":"first","affiliation":[]},{"given":"Soun-Hi","family":"Kwon","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2005,11,29]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"213","DOI":"10.4064\/aa106-3-2","article-title":"Bounds for the degrees of CM-fields of class number one","volume":"106","author":"Bessassi, Sofi\u00e8ne","year":"2003","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"issue":"9","key":"2","doi-asserted-by":"publisher","first-page":"2517","DOI":"10.1090\/S0002-9939-00-05555-6","article-title":"Class numbers of imaginary abelian number fields","volume":"128","author":"Chang, Ku-Young","year":"2000","journal-title":"Proc. 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