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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
MathSciNet review: 960644
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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. Lejeune Dirichlet, Vorlesungen über Zahlentheorie, Herausgegeben und mit Zusätzen versehen von R. Dedekind. Vierte, umgearbeitete und vermehrte Auflage, Chelsea Publishing Co., New York, 1968 (German). MR 0237283
  • [2] Kenneth Hardy and Kenneth S. Williams, The class number of pairs of positive-definite binary quadratic forms, Acta Arith. 52 (1989), no. 2, 103–117. MR 1005598
  • [3] Christopher Hooley, On the Diophantine equation 𝑎𝑥²+𝑏𝑦²+𝑐𝑧²+2𝑓𝑦𝑧+2𝑔𝑧𝑥+2ℎ𝑥𝑦=0, Arch. Math. (Basel) 19 (1968), 472–478. MR 0237430

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