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On Twisted Kloosterman Sums

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Abstract

For the Kloosterman sums twisted by characters over a finite field, addition formulas of convolution type are derived. As a corollary, orthogonality relations connecting the Kloosterman and Salie vectors are obtained. Bibliography: 4 titles.

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REFERENCES

  1. D. H. Lehmer and E. Lehmer, “The cyclotomy of Kloosterman sums,” Acta Arithm., 12, No.4, 385–407 (1967).

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  2. H. Salie, “Uber die Kloostermanschen Summen S(u, v; q),” Math. Z., 34, 91–109 (1931).

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  3. K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag (1990).

  4. K. S. Williams, “Note on Salie’s sum,” Proc. Amer. Math. Soc., 30, No.2, 393–394 (1971).

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 302, 2003, pp. 96–106.

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Proskurin, N.V. On Twisted Kloosterman Sums. J Math Sci 129, 3868–3873 (2005). https://doi.org/10.1007/s10958-005-0323-8

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