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Let k be a finite field of characteristic p, l a prime number different from p, $${\psi : k \to \overline{\bf Q}_l^\ast}$$ a nontrivial additive character, and $${\chi : {k^\ast}^n \to \overline{\bf Q}_l^\ast}$$ a character on $${{k^\ast}^n}$$ . Then ψ defines an Artin-Schreier sheaf $${\mathcal{L}_\psi}$$ on the affine line $${{\bf A}_k^1}$$ , and χ defines a Kummer sheaf ...
. Let m be a positive integer. Fix a nontrivial additive character ψ for each finite field Fq. To state the first result of this paper, we also fix r distinct multiplicative characters χ1,...,χr for each finite field Fq with more than r elements. We shall prove that when χ varies over multiplicative characters of Fq other than the m-th roots of the r-tuples of angles of Gauss sums are...
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