{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:43:34Z","timestamp":1776797014939,"version":"3.51.2"},"reference-count":11,"publisher":"American Mathematical Society (AMS)","issue":"287","license":[{"start":{"date-parts":[[2014,7,30]],"date-time":"2014-07-30T00:00:00Z","timestamp":1406678400000},"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                    The problem of characterization of rings whose elements can be expressed as sums of their units has a long history and is also of current interest. In this paper we take up the question of describing totally complex quartic number fields\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper 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                    with the property that every algebraic integer in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper 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                    is the sum of distinct units of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper 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                    . In particular, we give a short list containing all such fields.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2013-02751-2","type":"journal-article","created":{"date-parts":[[2013,7,30]],"date-time":"2013-07-30T13:55:49Z","timestamp":1375192549000},"page":"1495-1512","source":"Crossref","is-referenced-by-count":3,"title":["Distinct unit generated totally complex quartic fields"],"prefix":"10.1090","volume":"83","author":[{"given":"Lajos","family":"Hajdu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Volker","family":"Ziegler","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2013,7,30]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1112\/jlms\/s2-12.2.141","article-title":"A test for integers being sums of distinct units applied to cubic fields","volume":"12","author":"Belcher, Paul","year":"1975","journal-title":"J. London Math. Soc. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6107","issn-type":"print"},{"issue":"3-4","key":"2","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","article-title":"The Magma algebra system. I. The user language","volume":"24","author":"Bosma, Wieb","year":"1997","journal-title":"J. Symbolic Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0747-7171","issn-type":"print"},{"key":"3","first-page":"27","article-title":"On integral bases of pure quartic fields","volume":"26","author":"Funakura, Takeo","year":"1984","journal-title":"Math. J. Okayama Univ.","ISSN":"https:\/\/id.crossref.org\/issn\/0030-1566","issn-type":"print"},{"key":"4","doi-asserted-by":"publisher","first-page":"179","DOI":"10.2307\/2034028","article-title":"Sums of distinct divisors and sums of distinct units","volume":"15","author":"Jacobson, Bernard","year":"1964","journal-title":"Proc. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"},{"key":"5","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":"6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/jnth.1996.0031","article-title":"Certain quartic fields with small regulators","volume":"57","author":"Nakamula, Ken","year":"1996","journal-title":"J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-314X","issn-type":"print"},{"key":"7","series-title":"Monografie Matematyczne [Mathematical Monographs], Tom 57","volume-title":"Elementary and analytic theory of algebraic numbers","author":"Narkiewicz, W\u0142adys\u0142aw","year":"1974"},{"key":"8","first-page":"11","article-title":"Sums of distinct units","volume":"22","author":"\u015aliwa, J.","year":"1974","journal-title":"Bull. Acad. Polon. Sci. S\\'{e}r. Sci. Math. Astronom. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0001-4117","issn-type":"print"},{"key":"9","unstructured":"The PARI Group, Bordeaux. PARI\/GP, version 2.1.5, 2004. available from \\url{http:\/\/pari.math.u-bordeaux.fr\/}."},{"issue":"2","key":"10","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1112\/S0025579311001884","article-title":"On linear combinations of units with bounded coefficients","volume":"57","author":"Thuswaldner, J\u00f6rg","year":"2011","journal-title":"Mathematika","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5793","issn-type":"print"},{"key":"11","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"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2014-83-287\/S0025-5718-2013-02751-2\/S0025-5718-2013-02751-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2014-83-287\/S0025-5718-2013-02751-2\/S0025-5718-2013-02751-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T17:54:16Z","timestamp":1776794056000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2014-83-287\/S0025-5718-2013-02751-2\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7,30]]},"references-count":11,"journal-issue":{"issue":"287","published-print":{"date-parts":[[2014,5]]}},"alternative-id":["S0025-5718-2013-02751-2"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-2013-02751-2","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":[[2013,7,30]]}}}