{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:41:10Z","timestamp":1776840070197,"version":"3.51.2"},"reference-count":34,"publisher":"American Mathematical Society (AMS)","issue":"354","license":[{"start":{"date-parts":[[2025,8,14]],"date-time":"2025-08-14T00:00:00Z","timestamp":1755129600000},"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 give universal bounds on the fraction of nontrivial zeros having given multiplicity for\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                    -functions attached to a cuspidal automorphic representation of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper G normal upper L Subscript m Baseline slash double-struck upper Q\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi mathvariant=\"normal\">G<\/mml:mi>\n                                <mml:mi mathvariant=\"normal\">L<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mi>m<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\/<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Q<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathrm {GL}_m\/\\mathbb {Q}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . For this, we apply the higher-level correlation asymptotic of Hejhal, Rudnick, and Sarnak in conjunction with semidefinite programming bounds.\n                  <\/p>","DOI":"10.1090\/mcom\/4005","type":"journal-article","created":{"date-parts":[[2024,7,19]],"date-time":"2024-07-19T12:37:57Z","timestamp":1721392677000},"page":"2041-2058","source":"Crossref","is-referenced-by-count":0,"title":["Multiplicity of nontrivial zeros of primitive \ud835\udc3f-functions via higher-level correlations"],"prefix":"10.1090","volume":"94","author":[{"given":"Felipe","family":"Gon\u00e7alves","sequence":"first","affiliation":[]},{"given":"David","family":"de Laat","sequence":"additional","affiliation":[]},{"given":"Nando","family":"Leijenhorst","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2024,8,14]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"publisher","first-page":"813","DOI":"10.4171\/JEMS\/603","article-title":"Simple zeros of degree 2 \ud835\udc3f-functions","volume":"18","author":"Booker, Andrew R.","year":"2016","journal-title":"J. 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