note on the quadratic gauss sums
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ID: 211524
2001
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Abstract
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 sums G(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−1are
the eigenvalues of the circulant p×p matrix X with
elements the terms of the sequence {χ(m)}.
| Reference Key |
danas2001internationalnote
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|---|---|
| Authors | ;George Danas |
| Journal | structural engineering and mechanics |
| Year | 2001 |
| DOI |
10.1155/S016117120100480X
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| URL | |
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