Note on the Quadratic Gauss Sums
نویسنده
چکیده
Let p be an odd prime and {χ(m) = (m/p)}, m = 0,1, . . . ,p − 1 be a finite arithmetic sequence with elements the values of a Dirichlet character χ modp which are defined in terms of the Legendre symbol (m/p), (m,p)= 1. We study the relation between the Gauss and the quadratic Gauss sums. It is shown that the quadratic Gauss sumsG(k;p) are equal to the Gauss sums G(k,χ) that correspond to this particular Dirichlet character χ. Finally, using the above result, we prove that the quadratic Gauss sums G(k;p), k = 0,1, . . . ,p−1 are the eigenvalues of the circulant p×p matrix X with elements the terms of the sequence {χ(m)}. 2000 Mathematics Subject Classification. Primary 11L05; Secondary 11T24, 11L10.
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