{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T17:54:44Z","timestamp":1776794084675,"version":"3.51.2"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"276","license":[{"start":{"date-parts":[[2012,3,9]],"date-time":"2012-03-09T00:00:00Z","timestamp":1331251200000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this article, we report on computations that led to the discovery of a new Lehmer pair of zeros for the Riemann\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"zeta\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03b6\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\zeta<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    function. Given this new close pair of zeros, we improve the known lower bound for de Bruijn-Newman constant\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper Lamda\">\n                        <mml:semantics>\n                          <mml:mi mathvariant=\"normal\">\n                            \u039b\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\Lambda<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . The Riemann hypothesis is equivalent to the assertion\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper Lamda less-than-or-equal-to 0\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi mathvariant=\"normal\">\n                              \u039b\n                              \n                            <\/mml:mi>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\Lambda \\leq 0<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . In this article, we establish that in fact we have\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper Lamda greater-than negative 1.14541 times 10 Superscript negative 11\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi mathvariant=\"normal\">\n                              \u039b\n                              \n                            <\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mn>1.14541<\/mml:mn>\n                            <mml:mo>\n                              \u00d7\n                              \n                            <\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>10<\/mml:mn>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo>\n                                  \u2212\n                                  \n                                <\/mml:mo>\n                                <mml:mn>11<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\Lambda &gt; -1.14541 \\times 10^{-11}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . This new bound confirms the belief that if the Riemann hypothesis is true, it is barely true.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2011-02472-5","type":"journal-article","created":{"date-parts":[[2011,3,9]],"date-time":"2011-03-09T10:43:35Z","timestamp":1299667415000},"page":"2281-2287","source":"Crossref","is-referenced-by-count":11,"title":["An improved lower bound for the de Bruijn-Newman constant"],"prefix":"10.1090","volume":"80","author":[{"given":"Yannick","family":"Saouter","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xavier","family":"Gourdon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patrick","family":"Demichel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2011,3,9]]},"reference":[{"issue":"1-2","key":"1","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/S0377-0427(00)00336-8","article-title":"Computational strategies for the Riemann zeta function","volume":"121","author":"Borwein, Jonathan M.","year":"2000","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"issue":"5","key":"2","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1007\/BF01400887","article-title":"A lower bound for the de Bruijn-Newman constant \u039b","volume":"52","author":"Csordas, G.","year":"1988","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"3","first-page":"104","article-title":"A new Lehmer pair of zeros and a new lower bound for the de Bruijn-Newman constant \u039b","volume":"1","author":"Csordas, G.","year":"1993","journal-title":"Electron. Trans. Numer. Anal."},{"issue":"3","key":"4","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1007\/BF02142328","article-title":"The Laguerre inequalities with applications to a problem associated with the Riemann hypothesis","volume":"1","author":"Csordas, G.","year":"1991","journal-title":"Numer. 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