Recent progress in the study of representations of integers as sums of squares

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In this article, we collect the recent results concerning the representations of integers as sums of an even number of squares that are inspired by conjectures of Kac and Wakimoto. We start with a sketch of Milne's proof of two of these conjectures. We also show an alternative route to deduce these two conjectures from Milne's determinant formulas for sums of $4s^2$, respectively $4s(s+1)$, triangular numbers. This approach is inspired by Zagier's proof of the Kac--Wakimoto formulas via modular forms. We end the survey with recent conjectures of the first author and Chua.
11pages, AmS-LaTeX

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Number Theory, Classical Analysis and ODEs, 11D09 11E25

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http://salesiana.dossiersoluciones.com/handle/123456789/95869

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0407061
 http://arxiv.org/abs/math/0407061
 Bull. London Math. Soc. 37 (2005), 818-826.

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arXiv