{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T14:00:21Z","timestamp":1776866421284,"version":"3.51.2"},"reference-count":6,"publisher":"American Mathematical Society (AMS)","issue":"215","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We give new examples of real quadratic fields\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k\">\n                        <mml:semantics>\n                          <mml:mi>k<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for which the Iwasawa invariant\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda 3 left-parenthesis k right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03bb\n                                \n                              <\/mml:mi>\n                              <mml:mn>3<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda _3(k)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"mu 3 left-parenthesis k right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03bc\n                                \n                              <\/mml:mi>\n                              <mml:mn>3<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mu _3(k)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    are both zero by calculating cyclotomic units of real cyclic number fields of degree 18.\n                  <\/p>","DOI":"10.1090\/s0025-5718-96-00730-2","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"1339-1348","source":"Crossref","is-referenced-by-count":3,"title":["Cyclotomic units and Greenberg\u2019s conjecture for real quadratic fields"],"prefix":"10.1090","volume":"65","author":[{"given":"Takashi","family":"Fukuda","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"issue":"7","key":"1","first-page":"260","article-title":"Iwasawa\u2019s \ud835\udf06-invariants of certain real quadratic fields","volume":"65","author":"Fukuda, Takashi","year":"1989","journal-title":"Proc. Japan Acad. Ser. A Math. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0386-2194","issn-type":"print"},{"key":"2","doi-asserted-by":"crossref","unstructured":"T. Fukuda and H. Taya,  The Iwasawa \ud835\udf06-invariants of \u2124_{\ud835\udd61}-extensions of real quadratic fields, Acta Arith. 69 (1995), 277\u2013292.","DOI":"10.4064\/aa-69-3-277-292"},{"issue":"1","key":"3","doi-asserted-by":"publisher","first-page":"263","DOI":"10.2307\/2373625","article-title":"On the Iwasawa invariants of totally real number fields","volume":"98","author":"Greenberg, Ralph","year":"1976","journal-title":"Amer. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9327","issn-type":"print"},{"key":"4","first-page":"285","article-title":"Sur les inverses des \u00e9l\u00e9ments d\u00e9rivables dans un anneau abstrait","volume":"209","author":"Hebroni, P.","year":"1939","journal-title":"C. R. Acad. Sci. Paris","ISSN":"https:\/\/id.crossref.org\/issn\/0001-4036","issn-type":"print"},{"key":"5","series-title":"Lecture Notes in Mathematics","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0088938","volume-title":"The determination of units in real cyclic sextic fields","volume":"797","author":"M\u00e4ki, Sirpa","year":"1980","ISBN":"https:\/\/id.crossref.org\/isbn\/3540099840"},{"key":"6","doi-asserted-by":"crossref","unstructured":"H. Taya,  Computation of \u2124\u2083-invariants of real quadratic fields, Math. Comp. 65 (1996), 779\u2013784.","DOI":"10.1090\/S0025-5718-96-00721-1"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1996-65-215\/S0025-5718-96-00730-2\/S0025-5718-96-00730-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-215\/S0025-5718-96-00730-2\/S0025-5718-96-00730-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:13:17Z","timestamp":1776719597000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-215\/S0025-5718-96-00730-2\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996]]},"references-count":6,"journal-issue":{"issue":"215","published-print":{"date-parts":[[1996,7]]}},"alternative-id":["S0025-5718-96-00730-2"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-96-00730-2","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":[[1996]]}}}