{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:18:12Z","timestamp":1776784692902,"version":"3.51.2"},"reference-count":26,"publisher":"American Mathematical Society (AMS)","issue":"252","license":[{"start":{"date-parts":[[2006,3,31]],"date-time":"2006-03-31T00:00:00Z","timestamp":1143763200000},"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 present an algorithm for computing the cardinality of the Jacobian of a random Picard curve over a finite field. If the underlying field is a prime field\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper F Subscript p\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">F<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {F}_p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , the algorithm has complexity\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper O left-parenthesis StartRoot p EndRoot right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>O<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msqrt>\n                              <mml:mi>p<\/mml:mi>\n                            <\/mml:msqrt>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">O(\\sqrt {p})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-05-01758-8","type":"journal-article","created":{"date-parts":[[2005,8,10]],"date-time":"2005-08-10T10:23:21Z","timestamp":1123669401000},"page":"1983-2005","source":"Crossref","is-referenced-by-count":9,"title":["Point counting on Picard curves in large characteristic"],"prefix":"10.1090","volume":"74","author":[{"given":"Mark","family":"Bauer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Edlyn","family":"Teske","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Annegret","family":"Weng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2005,3,31]]},"reference":[{"issue":"245","key":"1","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1090\/S0025-5718-03-01559-X","article-title":"The arithmetic of certain cubic function fields","volume":"73","author":"Bauer, Mark L.","year":"2004","journal-title":"Math. 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A low-memory parallel version of Matsuo, Chao and Tsujii\u2019s algorithm. In Algorithmic Number Theory Symposium ANTS-VI, volume 3076 of Lecture Notes in Computer Science, pages 208\u2013222. Springer-Verlag, 2004.","DOI":"10.1007\/978-3-540-24847-7_15"},{"key":"9","series-title":"Pure and Applied Mathematics","isbn-type":"print","volume-title":"Principles of algebraic geometry","author":"Griffiths, Phillip","year":"1978","ISBN":"https:\/\/id.crossref.org\/isbn\/0471327921"},{"issue":"249","key":"10","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1090\/S0025-5718-04-01656-4","article-title":"Construction of CM Picard curves","volume":"74","author":"Koike, Kenji","year":"2005","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"11","unstructured":"[Mag] Computational Algebra Group. The Magma Computational Algebra System for Algebra, Number Theory and Geometry. School of Mathematics and Statistics, University of Sydney. http:\/\/magma.maths.usyd.edu.au\/magma."},{"key":"12","doi-asserted-by":"crossref","unstructured":"[Man65] Ju. I. Manin. The Hasse-Witt matrix of an algebraic curve. Trans. Amer. Math. Soc., 45:245-246, 1965.","DOI":"10.1090\/trans2\/045\/16"},{"key":"13","isbn-type":"print","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1007\/3-540-45455-1_36","article-title":"An improved baby step giant step algorithm for point counting of hyperelliptic curves over finite fields","author":"Matsuo, Kazuto","year":"2002","ISBN":"https:\/\/id.crossref.org\/isbn\/3540438637"},{"issue":"192","key":"14","doi-asserted-by":"publisher","first-page":"745","DOI":"10.2307\/2008445","article-title":"Frobenius maps of abelian varieties and finding roots of unity in finite fields","volume":"55","author":"Pila, J.","year":"1990","journal-title":"Math. 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Stein at the Conference in Number Theory in Honour of Professor H.C. Williams, Banff, May 2003."},{"issue":"238","key":"20","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1090\/S0025-5718-01-01385-0","article-title":"Explicit bounds and heuristics on class numbers in hyperelliptic function fields","volume":"71","author":"Stein, Andreas","year":"2002","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"238","key":"21","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1090\/S0025-5718-01-01343-6","article-title":"The parallelized Pollard kangaroo method in real quadratic function fields","volume":"71","author":"Stein, Andreas","year":"2002","journal-title":"Math. 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