{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:37:20Z","timestamp":1776724640823,"version":"3.51.2"},"reference-count":19,"publisher":"American Mathematical Society (AMS)","issue":"222","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    A detailed exposition of Kneser\u2019s neighbour method for quadratic lattices over totally real number fields, and of the sub-procedures needed for its implementation, is given. Using an actual computer program which automatically generates representatives for all isomorphism classes in one genus of rational lattices, various results about genera of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script l\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u2113\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\ell<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -elementary lattices, for small prime level\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script l comma\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>\n                              \u2113\n                              \n                            <\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\ell ,<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    are obtained. For instance, the class number of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"12\">\n                        <mml:semantics>\n                          <mml:mn>12<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">12<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -dimensional\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"7\">\n                        <mml:semantics>\n                          <mml:mn>7<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">7<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -elementary even lattices of determinant\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"7 Superscript 6\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mn>7<\/mml:mn>\n                            <mml:mn>6<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">7^6<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"395\">\n                        <mml:semantics>\n                          <mml:mn>395<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">395<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    ; no extremal lattice in the sense of Quebbemann exists. The implementation incorporates as essential parts previous programs of W.\u00a0Plesken and B.\u00a0Souvignier.\n                  <\/p>","DOI":"10.1090\/s0025-5718-98-00938-7","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"737-749","source":"Crossref","is-referenced-by-count":22,"title":["Classification of integral lattices with large class number"],"prefix":"10.1090","volume":"67","author":[{"given":"Rudolf","family":"Scharlau","sequence":"first","affiliation":[]},{"given":"Boris","family":"Hemkemeier","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1007\/BF02566012","article-title":"Voisinage au sens de Kneser pour les r\u00e9seaux quaternioniens","volume":"70","author":"Bachoc, Christine","year":"1995","journal-title":"Comment. Math. 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