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RECENT PROGRESS IN THE STUDY OF REPRESENTATIONS OF INTEGERS AS SUMS OF SQUARES

Published online by Cambridge University Press:  12 December 2005

HENG HUAT CHAN  and
CHRISTIAN KRATTENTHALER
HENG HUAT CHAN
Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, [email protected]
CHRISTIAN KRATTENTHALER
Affiliation:
Institut Girard Desargues, Université Claude Bernard Lyon-I, 21, avenue Claude Bernard, F-69622 Villeurbanne Cedex, France, [email protected]
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Abstract

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, $4s^2$ 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.

Keywords

11E2511F11
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 6 , December 2005 , pp. 818 - 826
Copyright
© The London Mathematical Society 2005

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