{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:44:39Z","timestamp":1776843879077,"version":"3.51.2"},"reference-count":12,"publisher":"American Mathematical Society (AMS)","issue":"280","license":[{"start":{"date-parts":[[2012,11,29]],"date-time":"2012-11-29T00:00:00Z","timestamp":1354147200000},"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>Here we present a Riemann-Siegel integral formula for the Lerch zeta function. Proceeding as in Turing\u2019s method for computing the Riemann zeta function, our integral formula allows for the numerical computation of the Lerch zeta function by numerical quadratures.<\/p>","DOI":"10.1090\/s0025-5718-2011-02566-4","type":"journal-article","created":{"date-parts":[[2011,11,30]],"date-time":"2011-11-30T13:46:03Z","timestamp":1322660763000},"page":"2319-2333","source":"Crossref","is-referenced-by-count":3,"title":["Riemann-Siegel integral formula for the Lerch zeta function"],"prefix":"10.1090","volume":"81","author":[{"given":"Eugenio","family":"Balanzario","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jorge","family":"S\u00e1nchez-Ortiz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2011,11,29]]},"reference":[{"issue":"1","key":"1","first-page":"1","article-title":"A Riemann-Siegel formula for the Hurwitz zeta function","volume":"10","author":"Balanzario, Eugenio P.","year":"2004","journal-title":"Bol. 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G.","year":"1958"},{"key":"5","series-title":"Pure and Applied Mathematics, Vol. 58","volume-title":"Riemann's zeta function","author":"Edwards, H. M.","year":"1974"},{"key":"6","isbn-type":"print","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1090\/conm\/290\/04575","article-title":"Computing the Riemann zeta function by numerical quadrature","author":"Galway, William F.","year":"2001","ISBN":"https:\/\/id.crossref.org\/isbn\/0821820796"},{"key":"7","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1017\/s0305004100024786","article-title":"The evaluation of integrals of the form \u222b^{\u221e}_{-\u221e}\ud835\udc53(\ud835\udc65)\ud835\udc52^{-\ud835\udc65\u00b2}\ud835\udc51\ud835\udc65","volume":"45","author":"Goodwin, E. T.","year":"1949","journal-title":"Proc. Cambridge Philos. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0008-1981","issn-type":"print"},{"key":"8","unstructured":"Lagarias, J.C.; Wen-Ching, Winnie Li, The Lerch zeta function I. Zeta integrals, Forum Mathematicum, published online."},{"key":"9","isbn-type":"print","volume-title":"The Lerch zeta-function","author":"Laurin\u010dikas, Antanas","year":"2002","ISBN":"https:\/\/id.crossref.org\/isbn\/1402010141"},{"issue":"1-4","key":"10","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/BF02418041","article-title":"Note sur la fonction \ud835\udd0e(\ud835\udd34,\ud835\udd35,\ud835\udd30)=\u2211_{\ud835\udd28=0}^{\u221e}\\frac{\ud835\udd22^{2\ud835\udd28\ud835\udf0b\ud835\udd26\ud835\udd35}}(\ud835\udd34+\ud835\udd28)^{\ud835\udd30}","volume":"11","author":"Lerch, M.","year":"1887","journal-title":"Acta Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0001-5962","issn-type":"print"},{"key":"11","doi-asserted-by":"publisher","first-page":"368","DOI":"10.2307\/2003759","article-title":"Error-bounds for the evaluation of integrals by the Euler-Maclaurin formula and by Gauss-type formulae","volume":"18","author":"McNamee, John","year":"1964","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"12","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1112\/plms\/s2-48.1.180","article-title":"A method for the calculation of the zeta-function","volume":"48","author":"Turing, A. M.","year":"1943","journal-title":"Proc. London Math. Soc. 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