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Brewet sums are finite numbers introduced by brewer related to Jacobsthal sums
In
mathematics, Brewer sums are finite
character sum introduced by Brewer (
1961,
1966) related to
Jacobsthal sums.
Definition
The Brewer sum is given by
where Dn is the
Dickson polynomial (or "Brewer polynomial") given by
and () is the
Legendre symbol.
The Brewer sum is zero when n is
coprime to q2−1.
References
- Brewer, B. W. (1961), "On certain character sums",
Transactions of the American Mathematical Society, 99 (2): 241–245,
doi:
10.2307/1993392,
ISSN
0002-9947,
JSTOR
1993392,
MR
0120202,
Zbl
0103.03205
- Brewer, B. W. (1966), "On primes of the form u²+5v²",
Proceedings of the American Mathematical Society, 17 (2): 502–509,
doi:
10.2307/2035200,
ISSN
0002-9939,
JSTOR
2035200,
MR
0188171,
Zbl
0147.29801
- Berndt, Bruce C.; Evans, Ronald J. (1979),
"Sums of Gauss, Eisenstein, Jacobi, Jacobsthal, and Brewer", Illinois Journal of Mathematics, 23 (3): 374–437,
doi:
10.1215/ijm/1256048104,
ISSN
0019-2082,
MR
0537798,
Zbl
0393.12029
- Lidl, Rudolf;
Niederreiter, Harald (1997),
Finite fields, Encyclopedia of Mathematics and Its Applications, vol. 20 (2nd ed.),
Cambridge University Press,
ISBN
0-521-39231-4,
Zbl
0866.11069