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Quadratic forms that represent almost the same primes
Author(s):
John
Voight.
Journal:
Math. Comp.
76
(2007),
1589-1617.
MSC (2000):
Primary 11E12;
Secondary 11E16, 11R11
Posted:
February 19, 2007
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Abstract:
Jagy and Kaplansky exhibited a table of  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
Email:
jvoight@gmail.com
DOI:
10.1090/S0025-5718-07-01976-X
PII:
S 0025-5718(07)01976-X
Keywords:
Binary quadratic forms,
number theory
Received by editor(s):
September 16, 2005
Received by editor(s) in revised form:
July 25, 2006
Posted:
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 of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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