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Kaplansky's ternary quadratic form

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  • James Kelley

Abstract

This paper proves that if N is a nonnegative eligible integer, coprime to 7, which is not of the form x 2 + y 2 + 7 z 2 , then N is square-free. The proof is modelled on that of a similar theorem by Ono and Soundararajan, in which relations between the number of representations of an integer n p 2 by two quadratic forms in the same genus, the p th coefficient of an L -function of a suitable elliptic curve, and the class number formula prove the theorem for large primes, leaving 3 cases which are easily numerically verified.

Suggested Citation

  • James Kelley, 2001. "Kaplansky's ternary quadratic form," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 25, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:650405
    DOI: 10.1155/S0161171201005294
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