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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Proving that a genus 2 curve has complex multiplication
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by Paul van Wamelen PDF
Math. Comp. 68 (1999), 1663-1677 Request permission

Abstract:

Recently examples of genus 2 curves defined over the rationals were found which, conjecturally, should have complex multiplication. We prove this conjecture. This involves computing an explicit representation of a rational map defining complex multiplication.
References
  • Henri Cohen, A course in computational algebraic number theory, Graduate Texts in Mathematics, vol. 138, Springer-Verlag, Berlin, 1993. MR 1228206, DOI 10.1007/978-3-662-02945-9
  • Erhard Gottschling, Explizite Bestimmung der Randflächen des Fundamentalbereiches der Modulgruppe zweiten Grades, Math. Ann. 138 (1959), 103–124 (German). MR 107020, DOI 10.1007/BF01342938
  • Gary Cornell and Joseph H. Silverman (eds.), Arithmetic geometry, Springer-Verlag, New York, 1986. Papers from the conference held at the University of Connecticut, Storrs, Connecticut, July 30–August 10, 1984. MR 861969, DOI 10.1007/978-1-4613-8655-1
  • David Mumford, Tata lectures on theta. II, Progress in Mathematics, vol. 43, Birkhäuser Boston, Inc., Boston, MA, 1984. Jacobian theta functions and differential equations; With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman and H. Umemura. MR 742776, DOI 10.1007/978-0-8176-4578-6
  • P. van Wamelen. Examples of genus two CM curves defined over the raionals, Math. Comp. 68 (1999), 307–320.
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Additional Information
  • Paul van Wamelen
  • Affiliation: Department of Mathematics, University of South Africa, P. O. Box 392, Pretoria, 0003, South Africa
  • Address at time of publication: Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803-4918
  • Email: wamelen@math.lsu.edu
  • Received by editor(s): December 16, 1997
  • Published electronically: May 17, 1999
  • Additional Notes: This work was partially supported by grant LEQSF(1995-97)-RD-A-09 from the Louisiana Educational Quality Support Fund.
  • © Copyright 1999 American Mathematical Society
  • Journal: Math. Comp. 68 (1999), 1663-1677
  • MSC (1991): Primary 14-04; Secondary 14K22
  • DOI: https://doi.org/10.1090/S0025-5718-99-01101-1
  • MathSciNet review: 1648415