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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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A simple derivation of Jacobi’s four-square formula
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by John A. Ewell PDF
Proc. Amer. Math. Soc. 85 (1982), 323-326 Request permission

Abstract:

For each nonnegative integer $n$, ${r_4}(n)$ counts number of solutions $({x_1},{x_2},{x_3},{x_4}) \in {{\mathbf {Z}}^4}{\text {of }}n = x_1^2 + x_2^2 + x_3^2 + x_4^2$. Within the confines of elementary partition theory the author presents a simple derivation of Jacobi’s formula for ${r_4}(n)$.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 323-326
  • MSC: Primary 10J05; Secondary 10A45
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0656093-9
  • MathSciNet review: 656093