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We develop all the necessary bounds, analyse the complexity of the algorithm and provide some examples computed with our implementation.<\/p>","DOI":"10.1090\/mcom\/2996","type":"journal-article","created":{"date-parts":[[2015,7,10]],"date-time":"2015-07-10T14:42:22Z","timestamp":1436539342000},"page":"961-981","source":"Crossref","is-referenced-by-count":18,"title":["Counting points on curves using a map to \ud835\udc0f\u00b9"],"prefix":"10.1090","volume":"85","author":[{"given":"Jan","family":"Tuitman","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2015,7,10]]},"reference":[{"key":"1","isbn-type":"print","first-page":"11","article-title":"Algebraic versus rigid cohomology with logarithmic coefficients","author":"Baldassarri, Francesco","year":"1994","ISBN":"https:\/\/id.crossref.org\/isbn\/0121972704"},{"issue":"1-3","key":"2","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1023\/A:1008323208670","article-title":"The Newton polygon of plane curves with many rational points","volume":"21","author":"Beelen, Peter","year":"2000","journal-title":"Des. 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Ramanujan Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0970-1249","issn-type":"print"},{"key":"12","isbn-type":"print","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1090\/conm\/463\/09047","article-title":"Search techniques for root-unitary polynomials","author":"Kedlaya, Kiran S.","year":"2008","ISBN":"https:\/\/id.crossref.org\/isbn\/9780821843208"},{"key":"13","doi-asserted-by":"publisher","first-page":"7","DOI":"10.4171\/RSMUP\/128-2","article-title":"Effective convergence bounds for Frobenius structures on connections","volume":"128","author":"Kedlaya, Kiran S.","year":"2012","journal-title":"Rend. Semin. Mat. Univ. Padova","ISSN":"https:\/\/id.crossref.org\/issn\/0041-8994","issn-type":"print"},{"key":"14","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1112\/S1461157000001261","article-title":"A recursive method for computing zeta functions of varieties","volume":"9","author":"Lauder, Alan G. B.","year":"2006","journal-title":"LMS J. Comput. 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Walker, Computing zeta functions of varieties via fibration, PhD thesis, Oxford, 2010."},{"key":"19","isbn-type":"print","doi-asserted-by":"publisher","first-page":"887","DOI":"10.1145\/2213977.2214056","article-title":"Multiplying matrices faster than Coppersmith-Winograd [extended abstract]","author":"Williams, Virginia Vassilevska","year":"2012","ISBN":"https:\/\/id.crossref.org\/isbn\/9781450312455"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2016-85-298\/S0025-5718-2015-02996-2\/S0025-5718-2015-02996-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2016-85-298\/S0025-5718-2015-02996-2\/S0025-5718-2015-02996-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:42:37Z","timestamp":1776796957000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2016-85-298\/S0025-5718-2015-02996-2\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,10]]},"references-count":19,"journal-issue":{"issue":"298","published-print":{"date-parts":[[2016,3]]}},"alternative-id":["S0025-5718-2015-02996-2"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/2996","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2015,7,10]]}}}