Evaluating prime power Gauss and Jacobi sums
نویسندگان
چکیده
منابع مشابه
On Gauss-Jacobi sums
In this paper, we introduce a kind of character sum which simultaneously generalizes the classical Gauss and Jacobi sums, and show that this “Gauss-Jacobi sum” also specializes to the Kloosterman sum in a particular case. Using the connection to the Kloosterman sums, we obtain in some special cases the upper bound (the “Weil bound”) of the absolute values of the Gauss-Jacobi sums. We also discu...
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In this paper we shall explore the structure of the ring of algebraic integers in any quadratic extension of the field of rational numbers Q, develop the concepts of Gauss and Jacobi sums, and apply the theory of algebraic integers and that of Gauss-Jacobi sums to solving problems involving power congruences and power sums as well as to proving the quadratic and cubic reciprocity laws. In parti...
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Using a sum-product result due to Bourgain, Katz, and Tao, we show that for every 0 < ǫ ≤ 1, and every power k ≥ 1, there exists an integer N = N(ǫ, k), such that for every prime p and every residue class a (mod p), there exist positive integers x1, ..., xN ≤ p ǫ satisfying a ≡ 1 x1 + · · · + 1 xN (mod p). This extends a result of I. Shparlinski [5].
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ژورنال
عنوان ژورنال: Tamkang Journal of Mathematics
سال: 2017
ISSN: 2073-9826,0049-2930
DOI: 10.5556/j.tkjm.48.2017.1866