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On a Product Related to the Cubic Gauss Sum, III

  • Hiroshi Ito (a1)

Abstract

We have seen, in the previous works [5], [6], that the argument of a certain product is closely connected to that of the cubic Gauss sum. Here the absolute value of the product will be investigated.

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References

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[1] Brinkhuis, J., Normal integral bases and complex conjugation. J. Reine Angew. Math. 375/376 (1987), 157166.
[2] Brinkhuis, J., On a comparison of Gauss sums with products of Lagrange resolvents. Compositio Math. 93 (1994), 155170.
[3] Fröhlich, A., Galois module structure of algebraic integers. Springer, 1983.
[4] Heath-Brown, D. R. and Patterson, S. J., The distribution of Kummer sums at prime arguments. J. Reine Angew. Math. 310 (1979), 111130.
[5] Ito, H., On a product related to the cubic Gauss sum. J. Reine Angew.Math. 395 (1989), 202213.
[6] Ito, H., On a product related to the cubic Gauss sum, II. Nagoya Math. J. 148 (1997), 121.
[7] Loxton, J. H., Products related to Gauss sums. J. Reine Angew.Math. 268/269 (1974), 202213.
[8] Matthews, C. R., Gauss sums and elliptic functions: I. The Kummer sum. Invent.Math. 52 (1979), 163185.
[9] McGettrick, A. D., A result in the theory of Weierstrass elliptic functions. Proc. LondonMath. Soc. (3) 25 (1972), 4154.
[10] Reshetukha, I. V., A product related to the cubic Gauss sum. Ukrainian Math. J. 37 (1985), 611616.
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On a Product Related to the Cubic Gauss Sum, III

  • Hiroshi Ito (a1)

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