Abstract
In this paper, we prove a conjecture of Chan and Chua for the number of representations of integers as sums of \(8s\) integral squares. The proof uses a theorem of Imamoḡlu and Kohnen, and the double shuffle relations satisfied by the double Eisenstein series of level 2.
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Acknowledgements
The author is grateful to Professor Masanobu Kaneko for initial advice and many useful comments over the course of this work. He also thanks Professor Winfried Kohnen and Professor Stephen Milne for their information and advice on the references.
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Tasaka, K. On a conjecture for representations of integers as sums of squares and double shuffle relations. Ramanujan J 33, 1–21 (2014). https://doi.org/10.1007/s11139-013-9513-z
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DOI: https://doi.org/10.1007/s11139-013-9513-z