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V . G . Kac and M . Wakimoto , ‘ Integrable highest weight modules over affine superalgebras and number theory ’ , Lie theory and geometry , in honor of Bertram Kostant , Progr
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Université Claude Bernard Lyon-I, 21, avenue Claude Bernard, F-69622 Villeurbanne Cedex, France E-mail address: kratt@euler.univ-lyon1
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In this article, the authors 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. They start with a sketch of Milne's proof of two of these conjectures, and they also show an alternative route to deduce these two conjectures from Milne's determinant formulas for sums of, respectively, 4s2 or 4s(s+1) triangular numbers. This approach is inspired by Zagier's proof of the Kac–Wakimoto formulas via modular forms. The survey ends with recent conjectures of the first author and Chua. 2000 Mathematics Subject Classification 11E25, 11F11.
Bulletin of the London Mathematical Society – Wiley
Published: Dec 1, 2005
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