Note on the quadratic Gauss sums
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 th...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120100480X |
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| Summary: | 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)}. |
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| ISSN: | 0161-1712 1687-0425 |