Cassels' Conjecture
A second conjecture on Kummer sums was made by J. W. S. Cassels, again building on previous ideas of Tomio Kubota. This was a product formula in terms of elliptic functions with complex multiplication by the Eisenstein integers. (J. W. S. Cassels, On Kummer sums, Proc. London Math. Soc., (3) 21 (1970), 19–27.) The conjecture was proved in 1978 by Charles Matthews. (C. R. Matthews, Gauss sums and elliptic functions: I. The Kummer sum. Invent. Math., 52 (1979), 163–185.)
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