{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T14:00:22Z","timestamp":1776866422740,"version":"3.51.2"},"reference-count":25,"publisher":"American Mathematical Society (AMS)","issue":"267","license":[{"start":{"date-parts":[[2010,1,28]],"date-time":"2010-01-28T00:00:00Z","timestamp":1264636800000},"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 study the Iwasawa\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03bb\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -invariant of the cyclotomic\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper Z 2\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Z<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {Z}_2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -extension of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper Q left-parenthesis StartRoot p EndRoot right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Q<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msqrt>\n                              <mml:mi>p<\/mml:mi>\n                            <\/mml:msqrt>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {Q}(\\sqrt {p} )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for an odd prime number\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                    which satisfies\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p identical-to 1 left-parenthesis mod 16 right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>\n                              \u2261\n                              \n                            <\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mspace width=\"0.667em\"\/>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>mod<\/mml:mi>\n                            <mml:mspace width=\"0.333em\"\/>\n                            <mml:mn>16<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">p\\equiv 1\\pmod {16}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    relating it to units having certain properties. We give an upper bound of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03bb\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and show\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda equals 0\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>\n                              \u03bb\n                              \n                            <\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda =0<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    in certain cases. We also give new numerical examples of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda equals 0\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>\n                              \u03bb\n                              \n                            <\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda =0<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-09-02124-3","type":"journal-article","created":{"date-parts":[[2009,4,27]],"date-time":"2009-04-27T13:47:33Z","timestamp":1240840053000},"page":"1797-1808","source":"Crossref","is-referenced-by-count":7,"title":["On the Iwasawa \ud835\udf06-invariant of the cyclotomic \u2124\u2082-extension of \u211a(\u221a\ud835\udd61)"],"prefix":"10.1090","volume":"78","author":[{"given":"Takashi","family":"Fukuda","sequence":"first","affiliation":[]},{"given":"Keiichi","family":"Komatsu","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2009,1,28]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1112\/S0025579300003703","article-title":"On the units of algebraic number fields","volume":"14","author":"Brumer, Armand","year":"1967","journal-title":"Mathematika","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5793","issn-type":"print"},{"issue":"2","key":"2","doi-asserted-by":"publisher","first-page":"377","DOI":"10.2307\/1971116","article-title":"The Iwasawa invariant \ud835\udf07_{\ud835\udc5d} vanishes for abelian number fields","volume":"109","author":"Ferrero, Bruce","year":"1979","journal-title":"Ann. of Math. 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J. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0040-8735","issn-type":"print"},{"key":"10","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1090\/S0002-9904-1959-10317-7","article-title":"On \u0393-extensions of algebraic number fields","volume":"65","author":"Iwasawa, Kenkichi","year":"1959","journal-title":"Bull. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9904","issn-type":"print"},{"key":"11","first-page":"1","article-title":"On the \ud835\udf07-invariants of \ud835\udc4d_{\u2113}-extensions","author":"Iwasawa, Kenkichi","year":"1973"},{"key":"12","doi-asserted-by":"publisher","first-page":"246","DOI":"10.2307\/1970784","article-title":"On \ud835\udc4d_{\ud835\udc59}-extensions of algebraic number fields","volume":"98","author":"Iwasawa, Kenkichi","year":"1973","journal-title":"Ann. of Math. 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J.","ISSN":"https:\/\/id.crossref.org\/issn\/0027-7630","issn-type":"print"},{"key":"17","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0853-2","volume-title":"Algebraic number theory","volume":"110","author":"Lang, Serge","year":"1994","ISBN":"https:\/\/id.crossref.org\/isbn\/0387942254","edition":"2"},{"issue":"1","key":"18","doi-asserted-by":"publisher","first-page":"255","DOI":"10.3836\/tjm\/1244208489","article-title":"On the Iwasawa invariants of \u2124\u2082-extensions of certain real quadratic fields","volume":"27","author":"Mizusawa, Yasushi","year":"2004","journal-title":"Tokyo J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0387-3870","issn-type":"print"},{"issue":"4","key":"19","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1007\/BF02677865","article-title":"On the Iwasawa \ud835\udf06\u2082-invariants of certain families of real quadratic fields","volume":"94","author":"Ozaki, Manabu","year":"1997","journal-title":"Manuscripta Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-2611","issn-type":"print"},{"key":"20","series-title":"DMV Seminar","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8589-8","volume-title":"Computational algebraic number theory","volume":"21","author":"Pohst, Michael E.","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/3764329130"},{"key":"21","isbn-type":"print","first-page":"53","article-title":"Computing invariants of algebraic number fields","author":"Pohst, Michael E.","year":"1996","ISBN":"https:\/\/id.crossref.org\/isbn\/3110153475"},{"issue":"9","key":"22","doi-asserted-by":"publisher","first-page":"3699","DOI":"10.1090\/S0002-9947-03-03357-9","article-title":"On the Iwasawa \ud835\udf06-invariants of real abelian fields","volume":"355","author":"Tsuji, Takae","year":"2003","journal-title":"Trans. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9947","issn-type":"print"},{"key":"23","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1934-7","volume-title":"Introduction to cyclotomic fields","volume":"83","author":"Washington, Lawrence C.","year":"1997","ISBN":"https:\/\/id.crossref.org\/isbn\/0387947620","edition":"2"},{"key":"24","series-title":"Die Grundlehren der mathematischen Wissenschaften, Band 144","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61945-8","volume-title":"Basic number theory","author":"Weil, Andr\u00e9","year":"1974","edition":"3"},{"issue":"3","key":"25","doi-asserted-by":"publisher","first-page":"493","DOI":"10.2307\/1971468","article-title":"The Iwasawa conjecture for totally real fields","volume":"131","author":"Wiles, A.","year":"1990","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2009-78-267\/S0025-5718-09-02124-3\/S0025-5718-09-02124-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-267\/S0025-5718-09-02124-3\/S0025-5718-09-02124-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:09:51Z","timestamp":1776787791000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-267\/S0025-5718-09-02124-3\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1,28]]},"references-count":25,"journal-issue":{"issue":"267","published-print":{"date-parts":[[2009,7]]}},"alternative-id":["S0025-5718-09-02124-3"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-09-02124-3","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":[[2009,1,28]]}}}