{"publisher":"American Mathematical Society","date_updated":"2026-05-04T15:32:12Z","date_created":"2026-05-04T15:31:12Z","author":[{"full_name":"Gundlach, Fabian","id":"100450","last_name":"Gundlach","first_name":"Fabian"}],"title":"Sampling cubic rings","doi":"10.1090/conm/840/16804","publication_status":"published","publication_identifier":{"isbn":["9781470485702","9781470480325"],"issn":["0271-4132","1098-3627"]},"place":"Providence, Rhode Island","year":"2026","citation":{"chicago":"Gundlach, Fabian. “Sampling Cubic Rings.” In <i>Contemporary Mathematics</i>. Providence, Rhode Island: American Mathematical Society, 2026. <a href=\"https://doi.org/10.1090/conm/840/16804\">https://doi.org/10.1090/conm/840/16804</a>.","ieee":"F. Gundlach, “Sampling cubic rings,” in <i>Contemporary Mathematics</i>, Providence, Rhode Island: American Mathematical Society, 2026.","bibtex":"@inbook{Gundlach_2026, place={Providence, Rhode Island}, title={Sampling cubic rings}, DOI={<a href=\"https://doi.org/10.1090/conm/840/16804\">10.1090/conm/840/16804</a>}, booktitle={Contemporary Mathematics}, publisher={American Mathematical Society}, author={Gundlach, Fabian}, year={2026} }","short":"F. Gundlach, in: Contemporary Mathematics, American Mathematical Society, Providence, Rhode Island, 2026.","mla":"Gundlach, Fabian. “Sampling Cubic Rings.” <i>Contemporary Mathematics</i>, American Mathematical Society, 2026, doi:<a href=\"https://doi.org/10.1090/conm/840/16804\">10.1090/conm/840/16804</a>.","ama":"Gundlach F. Sampling cubic rings. In: <i>Contemporary Mathematics</i>. American Mathematical Society; 2026. doi:<a href=\"https://doi.org/10.1090/conm/840/16804\">10.1090/conm/840/16804</a>","apa":"Gundlach, F. (2026). Sampling cubic rings. In <i>Contemporary Mathematics</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/conm/840/16804\">https://doi.org/10.1090/conm/840/16804</a>"},"_id":"65550","user_id":"100450","language":[{"iso":"eng"}],"type":"book_chapter","publication":"Contemporary Mathematics","abstract":[{"text":"<p>\r\n                    We explain how to construct a uniformly random cubic integral domain\r\n                    <inline-formula content-type=\"math/mathml\">\r\n                      <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S\">\r\n                        <mml:semantics>\r\n                          <mml:mi>S</mml:mi>\r\n                          <mml:annotation encoding=\"application/x-tex\">S</mml:annotation>\r\n                        </mml:semantics>\r\n                      </mml:math>\r\n                    </inline-formula>\r\n                    of given signature with\r\n                    <inline-formula content-type=\"math/mathml\">\r\n                      <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartAbsoluteValue d i s c left-parenthesis upper S right-parenthesis EndAbsoluteValue less-than-or-equal-to upper T\">\r\n                        <mml:semantics>\r\n                          <mml:mrow>\r\n                            <mml:mo fence=\"false\" stretchy=\"false\">\r\n                              |\r\n                              \r\n                            </mml:mo>\r\n                            <mml:mi>d</mml:mi>\r\n                            <mml:mi>i</mml:mi>\r\n                            <mml:mi>s</mml:mi>\r\n                            <mml:mi>c</mml:mi>\r\n                            <mml:mo stretchy=\"false\">(</mml:mo>\r\n                            <mml:mi>S</mml:mi>\r\n                            <mml:mo stretchy=\"false\">)</mml:mo>\r\n                            <mml:mo fence=\"false\" stretchy=\"false\">\r\n                              |\r\n                              \r\n                            </mml:mo>\r\n                            <mml:mo>\r\n                              ≤\r\n                              \r\n                            </mml:mo>\r\n                            <mml:mi>T</mml:mi>\r\n                          </mml:mrow>\r\n                          <mml:annotation encoding=\"application/x-tex\">\\lvert disc(S)\\rvert \\leq T</mml:annotation>\r\n                        </mml:semantics>\r\n                      </mml:math>\r\n                    </inline-formula>\r\n                    in expected time\r\n                    <inline-formula content-type=\"math/tex\">\r\n                      <tex-math>\\widetilde \\mathcal {O}(\\log T)</tex-math>\r\n                    </inline-formula>\r\n                    .\r\n                  </p>","lang":"eng"}],"status":"public"}