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

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

2004-07-05

arxiv.org/abs/math/0407061v1

Bull. London Math. Soc. 37 (2005), 818-826.

Mathematics

Number Theory

11pages, AmS-LaTeX

Scientific paper

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.

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