{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:43:18Z","timestamp":1776789798629,"version":"3.51.2"},"reference-count":21,"publisher":"American Mathematical Society (AMS)","issue":"266","license":[{"start":{"date-parts":[[2009,6,20]],"date-time":"2009-06-20T00:00:00Z","timestamp":1245456000000},"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 verify a very recent conjecture of Farmer and Rhoades on the asymptotic rate of growth of the derivatives of the Riemann xi function at\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"s equals 1 slash 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>s<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\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\">s=1\/2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We give two separate proofs of this result, with the more general method not restricted to\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"s equals 1 slash 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>s<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\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\">s=1\/2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We briefly describe other approaches to our results, give a heuristic argument, and mention supporting numerical evidence.\n                  <\/p>","DOI":"10.1090\/s0025-5718-08-02167-4","type":"journal-article","created":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T13:09:23Z","timestamp":1259672963000},"page":"1147-1154","source":"Crossref","is-referenced-by-count":5,"title":["Asymptotic estimation of \ud835\udf09\u207d\u00b2\u207f\u207e(1\/2): On a conjecture of Farmer and Rhoades"],"prefix":"10.1090","volume":"78","author":[{"given":"Mark","family":"Coffey","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2008,6,20]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1016\/j.cam.2003.09.003","article-title":"Relations and positivity results for the derivatives of the Riemann \ud835\udf09 function","volume":"166","author":"Coffey, Mark W.","year":"2004","journal-title":"J. Comput. Appl. 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Varga, A detailed numerical examination of the tracking of the zeros of \ud835\udc39_{\ud835\udf06}(\ud835\udc67) to produce a lower bound for the de Bruijn-Newman constant \u039b, ICM-9011-04 technical report (1990); http:\/\/icm.mcs.kent.edu\/reports."},{"key":"17","isbn-type":"print","volume-title":"The theory of the Riemann zeta-function","author":"Titchmarsh, E. C.","year":"1986","ISBN":"https:\/\/id.crossref.org\/isbn\/0198533691","edition":"2"},{"key":"18","series-title":"CBMS-NSF Regional Conference Series in Applied Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970111","volume-title":"Scientific computation on mathematical problems and conjectures","volume":"60","author":"Varga, Richard S.","year":"1990","ISBN":"https:\/\/id.crossref.org\/isbn\/0898712572"},{"key":"19","doi-asserted-by":"crossref","unstructured":"A. Wintner, A note on the Riemann \ud835\udf09-function, J. London Math. 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