{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:38:13Z","timestamp":1776800293176,"version":"3.51.2"},"reference-count":28,"publisher":"American Mathematical Society (AMS)","issue":"300","license":[{"start":{"date-parts":[[2016,11,9]],"date-time":"2016-11-09T00:00:00Z","timestamp":1478649600000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["BR-2163\/4-1"],"award-info":[{"award-number":["BR-2163\/4-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["BR-2163\/4-1"],"award-info":[{"award-number":["BR-2163\/4-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["BR-2163\/4-1"],"award-info":[{"award-number":["BR-2163\/4-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["BR-2163\/4-1"],"award-info":[{"award-number":["BR-2163\/4-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We prove that there are only finitely many isometry classes of even lattices\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L\">\n                        <mml:semantics>\n                          <mml:mi>L<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">L<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of signature\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-parenthesis 2 comma n right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">(2,n)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for which the space of cusp forms of weight\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"1 plus n slash 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\/<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">1+n\/2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for the Weil representation of the discriminant group of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L\">\n                        <mml:semantics>\n                          <mml:mi>L<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">L<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is trivial. We compute the list of these lattices. They have the property that every Heegner divisor for the orthogonal group of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L\">\n                        <mml:semantics>\n                          <mml:mi>L<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">L<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    can be realized as the divisor of a Borcherds product. We obtain similar classification results in greater generality for finite quadratic modules.\n                  <\/p>","DOI":"10.1090\/mcom\/3059","type":"journal-article","created":{"date-parts":[[2015,5,13]],"date-time":"2015-05-13T11:16:09Z","timestamp":1431515769000},"page":"1953-1981","source":"Crossref","is-referenced-by-count":13,"title":["Lattices with many Borcherds products"],"prefix":"10.1090","volume":"85","author":[{"given":"Jan","family":"Bruinier","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephan","family":"Ehlen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eberhard","family":"Freitag","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,11,9]]},"reference":[{"key":"1","isbn-type":"print","volume-title":"Pocketbook of mathematical functions","year":"1984","ISBN":"https:\/\/id.crossref.org\/isbn\/3871448184"},{"issue":"3","key":"2","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1007\/s002220050232","article-title":"Automorphic forms with singularities on Grassmannians","volume":"132","author":"Borcherds, Richard E.","year":"1998","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"issue":"2","key":"3","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1215\/S0012-7094-99-09710-7","article-title":"The Gross-Kohnen-Zagier theorem in higher dimensions","volume":"97","author":"Borcherds, Richard E.","year":"1999","journal-title":"Duke Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0012-7094","issn-type":"print"},{"issue":"2","key":"4","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1215\/S0012-7094-00-10424-3","article-title":"Reflection groups of Lorentzian lattices","volume":"104","author":"Borcherds, Richard E.","year":"2000","journal-title":"Duke Math. 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