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Let be a finite arithmetic sequence in C with elements the values of a Dirichlet character Ξ mod n. If Xis the circulant n × n matrix with elements Ξ(i) then the eigenvalues of X are the Gauss sums
that correspond to Ξ. Moreover, if Ξ=Ξ1 is the principal Dirichlet character mod n, then the eigenvalues of X are the Ramanujan sums C
n(K).
1991 Mathematics Subject Classification:
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