{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T13:12:50Z","timestamp":1776863570959,"version":"3.51.2"},"reference-count":38,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2015,8,1]],"date-time":"2015-08-01T00:00:00Z","timestamp":1438387200000},"content-version":"unspecified","delay-in-days":212,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>We show how to efficiently evaluate functions on Jacobian varieties and their quotients. We deduce an algorithm to compute<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157015000169_inline1\"\/><jats:tex-math>$(l,l)$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>isogenies between Jacobians of genus two curves in quasi-linear time in the degree<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157015000169_inline2\"\/><jats:tex-math>$l^{2}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1112\/s1461157015000169","type":"journal-article","created":{"date-parts":[[2015,8,25]],"date-time":"2015-08-25T04:37:50Z","timestamp":1440477470000},"page":"555-577","source":"Crossref","is-referenced-by-count":15,"title":["Computing functions on Jacobians and their quotients"],"prefix":"10.1112","volume":"18","author":[{"given":"Jean-Marc","family":"Couveignes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tony","family":"Ezome","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2015,8,1]]},"reference":[{"key":"S1461157015000169_r33","unstructured":"33. The PARI\u00a0Group, Bordeaux. PARI\/GP version 2.7.2, 2014, available fromhttp:\/\/pari.math.u-bordeaux.fr\/."},{"key":"S1461157015000169_r10","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1515\/9781400839001.69","volume-title":"Computational aspects of modular forms and Galois representations","author":"Couveignes","year":"2011"},{"key":"S1461157015000169_r16","doi-asserted-by":"crossref","first-page":"589","DOI":"10.17323\/1609-4514-2002-2-3-589-631","article-title":"\u00c9tale cohomology, Lefschetz theorems and number of points of singular varieties over finite fields","volume":"2","author":"Ghorpade","year":"2002","journal-title":"Mosc. Math. J."},{"key":"S1461157015000169_r12","first-page":"51","volume-title":"Curves and abelian\u00a0varieties","author":"Dolgachev","year":"2008"},{"key":"S1461157015000169_r3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-06307-1"},{"key":"S1461157015000169_r27","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8655-1_5"},{"key":"S1461157015000169_r2","doi-asserted-by":"crossref","DOI":"10.3792\/chmm\/1428686976","volume-title":"Abel\u2019s theorem and the allied theory, including the theory of the theta functions","author":"Baker","year":"1897"},{"key":"S1461157015000169_r18","unstructured":"18. A. Joux and R. Lercier , \u2018Counting points on elliptic curves in medium characteristic\u2019. Cryptology ePrint Archive, Report 2006\/176, 2006."},{"key":"S1461157015000169_r28","volume-title":"Tata lectures on theta. III, Modern Birkh\u00e4user classics","author":"Mumford","year":"2007"},{"key":"S1461157015000169_r34","first-page":"A238","article-title":"Isog\u00e9nies entre courbes elliptiques","volume":"273","author":"V\u00e9lu","year":"1971","journal-title":"C. R. Acad. Sci. Paris"},{"key":"S1461157015000169_r9","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1515\/9781400839001.337","volume-title":"Computational aspects of modular forms and Galois representations","author":"Couveignes","year":"2011"},{"key":"S1461157015000169_r31","unstructured":"31. N. Shepherd-Barron , \u2018Thomae\u2019s formulae for non-hyperelliptic curves and spinorial square roots of theta-constants on the moduli space of curves\u2019, Preprint, 2008, arXiv:0802.3014."},{"key":"S1461157015000169_r15","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1145\/2608628.2608664","volume-title":"ISSAC 2014 Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation","author":"Le Gall","year":"2014"},{"key":"S1461157015000169_r1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-5323-3"},{"key":"S1461157015000169_r26","doi-asserted-by":"publisher","DOI":"10.1007\/s00145-004-0315-8"},{"key":"S1461157015000169_r19","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-07-01989-8"},{"key":"S1461157015000169_r30","doi-asserted-by":"publisher","DOI":"10.5802\/jtnb.142"},{"key":"#cr-split#-S1461157015000169_r29.1","unstructured":"4. D. Mumford\u00a0 Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics 5 (Published for the Tata Institute of Fundamental Research, Bombay, 2008)"},{"key":"#cr-split#-S1461157015000169_r29.2","unstructured":"5. with appendices by C. P. Ramanujam\u00a0and Y. Manin. Corrected reprint of the second 1974 edition."},{"key":"S1461157015000169_r22","first-page":"77","volume-title":"Computational perspectives on number theory: proceedings of a conference in honor of A. O. L. Atkin","author":"Lercier","year":"1998"},{"key":"S1461157015000169_r7","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2014-02899-8"},{"key":"S1461157015000169_r17","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.2001.0513"},{"key":"S1461157015000169_r11","unstructured":"11. C. Diem , \u2018On arithmetic and the discrete logarithm problem in class groups of curves\u2019, Habilitation Thesis, Leipzig, 2008."},{"key":"S1461157015000169_r35","first-page":"5","article-title":"Courbes elliptiques munies d\u2019un sous-groupe Z\u2215n Z \u00d7\ud835\udf07 n","volume":"57","author":"V\u00e9lu","year":"1978","journal-title":"Bull. Soc. Math. France M\u00e9m."},{"key":"S1461157015000169_r14","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0060090"},{"key":"S1461157015000169_r20","doi-asserted-by":"crossref","first-page":"329","DOI":"10.4064\/aa-56-4-329-340","article-title":"Nombre de points des jacobiennes sur un corps fini","volume":"56","author":"Lachaud","year":"1990","journal-title":"Acta Arith."},{"key":"S1461157015000169_r24","doi-asserted-by":"publisher","DOI":"10.1112\/S146115701400045X"},{"key":"S1461157015000169_r4","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-08-02066-8"},{"key":"S1461157015000169_r6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03338-8"},{"key":"S1461157015000169_r8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2008.09.032"},{"key":"S1461157015000169_r13","first-page":"21","volume-title":"Computational perspectives on number theory (Chicago, IL, 1995)","author":"Elkies","year":"1998"},{"key":"S1461157015000169_r21","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8534-7"},{"key":"S1461157015000169_r25","doi-asserted-by":"publisher","DOI":"10.1007\/s12215-013-0136-4"},{"key":"S1461157015000169_r23","doi-asserted-by":"publisher","DOI":"10.1112\/S0010437X12000243"},{"key":"S1461157015000169_r36","volume-title":"Actualit\u00e9s Sci. Ind., no. 1041","author":"Weil","year":"1948"},{"key":"S1461157015000169_r37","volume-title":"Actualit\u00e9s Sci. Ind., no. 1064","author":"Weil","year":"1948"},{"key":"S1461157015000169_r5","doi-asserted-by":"publisher","DOI":"10.1145\/322092.322099"},{"key":"S1461157015000169_r32","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/574\/11418"}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1461157015000169","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,13]],"date-time":"2023-08-13T11:19:18Z","timestamp":1691925558000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1461157015000169\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015]]}},"alternative-id":["S1461157015000169"],"URL":"https:\/\/doi.org\/10.1112\/s1461157015000169","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]}}}