منابع مشابه
Several generalizations of Weil sums
We consider several generalizations and variations of the character sum inequalities of Weil and Burgess. A number of incomplete character sum inequalities are proved while further conjectures are formulated. These inequalities are motivated by extremal graph theory with applications to problems in computer science.
متن کاملDivisibility of Weil Sums of Binomials
Consider the Weil sumWF,d(u) = ∑ x∈F ψ(x +ux), where F is a finite field of characteristic p, ψ is the canonical additive character of F , d is coprime to |F |, and u ∈ F . We say that WF,d(u) is threevalued when it assumes precisely three distinct values as u runs through F : this is the minimum number of distinct values in the nondegenerate case, and three-valuedWF,d are rare and desirable. W...
متن کاملCyclotomy of Weil Sums of Binomials
The Weil sum WK,d(a) = ∑ x∈K ψ(x d + ax) where K is a finite field, ψ is an additive character of K, d is coprime to |K|, and a ∈ K arises often in number-theoretic calculations, and in applications to finite geometry, cryptography, digital sequence design, and coding theory. Researchers are especially interested in the case where WK,d(a) assumes three distinct values as a runs through K. A Gal...
متن کاملA note on evaluations of some exponential sums
where χ is a non-trivial additive character of the finite field Fq, q = p odd, and a ∈ Fq . In my dissertation [5], in particular in [4], I considered more generally the sums S(a,N) for all factors N of p+1. The aim of the present note is to evaluate S(a,N) in a short way, following [4]. We note that our result is also valid for even q, and the technique used in our proof can also be used to ev...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1998
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-86-3-217-226