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Bull. London Math. Soc. 37 (2005), 818-826,
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Recent progress in the study of representations of
integers as sums of squares
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 4s2,
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
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