On a conjecture for representations of integers as sums of squares and double shuffle relations. (English) Zbl 1392.11021
Summary: In this paper, we prove a conjecture of H. H. Chan and K. S. Chua [Ramanujan J. 7, No. 1-3, 79–89 (2003; Zbl 1031.11022)] for the number of representations of integers as sums of \(8s\) integral squares. The proof uses a theorem of Ö. Imamoḡlu and W. Kohnen [Math. Ann. 333, No. 4, 815–829 (2005; Zbl 1081.11026)], and the double shuffle relations satisfied by the double Eisenstein series of level 2.
MSC:
| 11D85 | Representation problems |
| 11M32 | Multiple Dirichlet series and zeta functions and multizeta values |
| 11E25 | Sums of squares and representations by other particular quadratic forms |
| 11F27 | Theta series; Weil representation; theta correspondences |
References:
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