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Trees, maximal orders and integral quadratic forms. (Arbres, ordres maximaux et formes quadratiques entières.) (French) Zbl 0826.11016

David, Sinnou (ed.), Number theory. Séminaire de théorie des nombres de Paris 1992-93. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 215, 209-230 (1995).
The paper presents a proof of Jacobi’s formula for the number of representations of an integer as the sum of 4 squares. The proof uses actions of groups of quaternions on the tree of \(\text{SL}_2 (\mathbb Q_p)\) and is expanded from scratch, so that it is accessible to a student with background in algebra.
For the entire collection see [Zbl 0814.00015].

MSC:

11E25 Sums of squares and representations by other particular quadratic forms
11R52 Quaternion and other division algebras: arithmetic, zeta functions
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