{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T00:14:08Z","timestamp":1779322448362,"version":"3.51.4"},"publisher-location":"Berlin, Heidelberg","reference-count":19,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540360759","type":"print"},{"value":"9783540360766","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1007\/11792086_12","type":"book-chapter","created":{"date-parts":[[2006,10,4]],"date-time":"2006-10-04T09:48:35Z","timestamp":1159955315000},"page":"156-167","source":"Crossref","is-referenced-by-count":11,"title":["The Mertens Conjecture Revisited"],"prefix":"10.1007","author":[{"given":"Tadej","family":"Kotnik","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Herman","family":"te Riele","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"12_CR1","unstructured":"Bateman, P.T., Brown, J.W., Hall, R.S., Kloss, K.E., Stemmler, R.M.: Linear relations connecting the imaginary parts of the zeros of the zeta function. In: Atkin, A.O.L., Birch, B.J. (eds.) Computers in Number Theory, New York, pp. 11\u201319 (1971)"},{"key":"12_CR2","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1112\/S0024611502013655","volume":"85","author":"K. Ford","year":"2002","unstructured":"Ford, K.: Vinogradov\u2019s integral and bounds for the Riemann zeta function. Proc. Lond. Math. Soc.\u00a085, 565\u2013633 (2002)","journal-title":"Proc. Lond. Math. Soc."},{"key":"12_CR3","doi-asserted-by":"publisher","first-page":"857","DOI":"10.2307\/2004584","volume":"22","author":"I.J. Good","year":"1968","unstructured":"Good, I.J., Churchhouse, R.F.: The Riemann hypothesis and pseudorandom features of the M\u00f6bius sequence. Math. Comp.\u00a022, 857\u2013861 (1968)","journal-title":"Math. Comp."},{"key":"12_CR4","unstructured":"Hardy, G.H., Wright, E.M.: An introduction to the theory of numbers, 4th edn. Oxford at the Clarendon Press (1975)"},{"key":"12_CR5","doi-asserted-by":"publisher","first-page":"313","DOI":"10.2307\/2371685","volume":"64","author":"A.E. Ingham","year":"1942","unstructured":"Ingham, A.E.: On two conjectures in the theory of numbers. Amer. J. Math.\u00a064, 313\u2013319 (1942)","journal-title":"Amer. J. Math."},{"key":"12_CR6","doi-asserted-by":"crossref","unstructured":"Jurkat, W.B.: On the Mertens conjecture and related general \u03a9-theorems. In: Diamond, H. (ed.) Analytic Number Theory, Providence, pp. 147\u2013158 (1973)","DOI":"10.1090\/pspum\/024\/0352026"},{"key":"12_CR7","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1515\/crll.1976.286-287.322","volume":"286\/287","author":"W. Jurkat","year":"1976","unstructured":"Jurkat, W., Peyerimhoff, A.: A constructive approach to Kronecker approximations and its application to the Mertens conjecture. J. reine angew. Math.\u00a0286\/287, 322\u2013340 (1976)","journal-title":"J. reine angew. Math."},{"key":"12_CR8","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1080\/10586458.2004.10504556","volume":"13","author":"T. Kotnik","year":"2004","unstructured":"Kotnik, T., van de Lune, J.: On the order of the Mertens function. Exp. Math.\u00a013, 473\u2013481 (2004)","journal-title":"Exp. Math."},{"key":"12_CR9","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1007\/BF01457454","volume":"261","author":"A.K. Lenstra","year":"1982","unstructured":"Lenstra, A.K., Lenstra Jr., H.W., Lov\u00e1sz, L.: Factoring polynomials with rational coefficients. Math. Ann.\u00a0261, 515\u2013534 (1982)","journal-title":"Math. Ann."},{"key":"12_CR10","unstructured":"Mathematica, version 5.0, Wolfram Research, Inc., Champaign, IL (2003), http:\/\/www.wolfram.com\/"},{"key":"12_CR11","first-page":"761","volume":"106","author":"F. Mertens","year":"1897","unstructured":"Mertens, F.: \u00dcber eine zahlentheoretische Funktion. Sitzungsberichte Akad. Wiss. Wien IIa\u00a0106, 761\u2013830 (1897)","journal-title":"Sitzungsberichte Akad. Wiss. Wien IIa"},{"key":"12_CR12","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1112\/S0024611504014741","volume":"89","author":"N. Ng","year":"2004","unstructured":"Ng, N.: The distribution of the summatory function of the M\u00f6bius function. Proc. Lond. Math. Soc.\u00a089, 361\u2013389 (2004)","journal-title":"Proc. Lond. Math. Soc."},{"key":"12_CR13","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1515\/crll.1985.357.138","volume":"357","author":"A.M. Odlyzko","year":"1985","unstructured":"Odlyzko, A.M., te Riele, H.J.J.: Disproof of the Mertens conjecture. J. reine angew. Math.\u00a0357, 138\u2013160 (1985)","journal-title":"J. reine angew. Math."},{"key":"12_CR14","first-page":"325","volume":"147\u2013148","author":"J. Pintz","year":"1987","unstructured":"Pintz, J.: An effective disproof of the Mertens conjecture. Ast\u00e9risque\u00a0147\u2013148, 325\u2013333 (1987)","journal-title":"Ast\u00e9risque"},{"key":"12_CR15","unstructured":"PARI\/GP, version 2.2.11 (alpha), Bordeaux (2005), http:\/\/pari.math.u-bordeaux.fr\/"},{"key":"12_CR16","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1515\/crll.1979.311-312.356","volume":"311\/312","author":"H.J.J. Riele te","year":"1979","unstructured":"te Riele, H.J.J.: Computations concerning the conjecture of Mertens. J. reine angew. Math.\u00a0311\/312, 356\u2013360 (1979)","journal-title":"J. reine angew. Math."},{"issue":"A","key":"12_CR17","first-page":"1097","volume":"271","author":"B. Saffari","year":"1970","unstructured":"Saffari, B.: Sur la fausset\u00e9 de la conjecture de Mertens. Avec une observation par Paul L\u00e9vy. C. R. Acad. Sci.\u00a0271(A), 1097\u20131101 (1970)","journal-title":"C. R. Acad. Sci."},{"key":"12_CR18","unstructured":"Titchmarsh, E.C.: The Theory of the Riemann Zeta-Function, Oxford (1951)"},{"key":"12_CR19","unstructured":"Walfisz, A.: Weylsche Exponentialsummen in der neueren Zahlentheorie. VEB Deutscher Verlag (1963)"}],"container-title":["Lecture Notes in Computer Science","Algorithmic Number Theory"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11792086_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,21]],"date-time":"2019-04-21T08:50:06Z","timestamp":1555836606000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11792086_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9783540360759","9783540360766"],"references-count":19,"URL":"https:\/\/doi.org\/10.1007\/11792086_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006]]}}}