Brewer sum

Template:Short description In mathematics, Brewer sums are finite character sum introduced by Template:Harvs related to Jacobsthal sums.

Definition

The Brewer sum is given by

${\mathrm{\Lambda }}_n(a)=\sum _{xmodp}(\genfrac{}{}{0ex}{}{D_{n+1}(x,a)}{p})$

where D_n is the Dickson polynomial (or "Brewer polynomial") given by

$D_0(x,a)=2,D_1(x,a)=x,D_{n+1}(x,a)=x{D}_n(x,a)-a{D}_{n-1}(x,a)$

and () is the Legendre symbol.

The Brewer sum is zero when n is coprime to q²−1.

References

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