Brewer sum - Alchetron, The Free Social Encyclopedia

In mathematics, Brewer sums are finite character sum introduced by Brewer (1961, 1966) related to Jacobsthal sums.

Definition

The Brewer sum is given by

Λ n ( a ) = ∑ x mod p ( 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 )

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

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