Representation of a binary quadratic form as a sum of two squares

Williams, Kenneth S.

doi:10.1090/S0002-9939-1972-0325536-6

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Representation of a binary quadratic form as a sum of two squares
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by Kenneth S. Williams PDF

Proc. Amer. Math. Soc. 32 (1972), 368-370 Request permission

Abstract:

Let $\phi (x,y)$ be an integral binary quadratic form. A short proof is given of Pall’s formula for the number of representations of $\phi (x,y)$ as the sum of squares of two integral linear forms.

References

L. J. Mordell, On the representation of a binary quadratic form as a sum of squares of linear forms, Math. Z. 35 (1932), no. 1, 1–15. MR 1545284, DOI 10.1007/BF01186544
Gordon Pall, Sums of two squares in a quadratic field, Duke Math. J. 18 (1951), 399–409. MR 40337