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

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dc.creatorChan, Heng Huat
dc.creatorKrattenthaler, Christian
dc.date2004-07-05
dc.date.accessioned2026-07-07T06:22:18Z
dc.date.available2026-07-07T06:22:18Z
dc.descriptionIn 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.
dc.description11pages, AmS-LaTeX
dc.identifierhttps://arxiv.org/abs/math/0407061
dc.identifierhttp://arxiv.org/abs/math/0407061
dc.identifierBull. London Math. Soc. 37 (2005), 818-826.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95869
dc.subjectNumber Theory
dc.subjectClassical Analysis and ODEs
dc.subject11D09 11E25
dc.titleRecent progress in the study of representations of integers as sums of squares
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