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The representation of a pair of integers by a pair of positive-definite binary quadratic forms


Authors: Kenneth Hardy, Pierre Kaplan and Kenneth S. Williams
Journal: Proc. Amer. Math. Soc. 105 (1989), 847-855
MSC: Primary 11E16; Secondary 11D85
DOI: https://doi.org/10.1090/S0002-9939-1989-0960644-0
MathSciNet review: 960644
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Abstract | References | Similar Articles | Additional Information

Abstract: An explicit formula is given for the number of representations of a pair of positive integers by a representative set of inequivalent pairs of integral positive-definite binary quadratic forms with given invariants.


References [Enhancements On Off] (What's this?)

  • [1] P. G. L. Dirichlet, Vorlesungen über Zahlentheorie, reprinted 4th edition, Chelsea Publishing Company, New York, 1968, p. 229. MR 0237283 (38:5573)
  • [2] K. Hardy and K. S. Williams, The class number of pairs of positive-definite binary quadratic forms, Acta Arithmetica (to appear). MR 1005598 (90g:11049)
  • [3] C. Hooley, On the diophantine equation $ a{x^2} + b{y^2} + c{z^2} + 2fyz + 2gzx + 2hxy = 0$, Arch. Math. 19 (1968), 472-478. MR 0237430 (38:5712)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0960644-0
Article copyright: © Copyright 1989 American Mathematical Society

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