Eisenstein sum

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Not to be confused with Eisenstein series.

In mathematics, an Eisenstein sum is a finite sum depending on a finite field and related to a Gauss sum. Eisenstein sums were introduced by Gotthold Eisenstein (1848), named "Eisenstein sums" by Stickelberger (1890), and rediscovered by Yamamoto (1985), who called them relative Gauss sums.

Definition[edit]

The Eisenstein sum is given by

E(\chi,\alpha)=\sum_{Tr_{F/K}t=\alpha}\chi(t)

where F is a finite extension of the finite field K, and χ is a character of the multiplicative group of F, and α is an element of K (Lemmermeyer 2000, p. 133).

References[edit]