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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Quadratic forms that represent almost the same primes
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by John Voight PDF
Math. Comp. 76 (2007), 1589-1617 Request permission

Abstract:

Jagy and Kaplansky exhibited a table of $68$ pairs of positive definite binary quadratic forms that represent the same odd primes and conjectured that their list is complete outside of “trivial” pairs. In this article, we confirm their conjecture, and in fact find all pairs of such forms that represent the same primes outside of a finite set.
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Additional Information
  • John Voight
  • Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
  • Address at time of publication: Institute for Mathematics and its Applications, 400 Lind Hall, 237 Church Street, University of Minnesota, Minneapolis, Minnesota 55455
  • MR Author ID: 727424
  • ORCID: 0000-0001-7494-8732
  • Email: jvoight@gmail.com
  • Received by editor(s): September 16, 2005
  • Received by editor(s) in revised form: July 25, 2006
  • Published electronically: February 19, 2007
  • Additional Notes: The author’s research was partially supported by an NSF Graduate Fellowship. The author would like to thank Hendrik Lenstra, Peter Stevenhagen, and the reviewer for their helpful comments, as well as William Stein and the MECCAH cluster for computer time
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 76 (2007), 1589-1617
  • MSC (2000): Primary 11E12; Secondary 11E16, 11R11
  • DOI: https://doi.org/10.1090/S0025-5718-07-01976-X
  • MathSciNet review: 2299790