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
The Eisenstein sum is given by
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
Eisenstein sum Wikipedia(Text) CC BY-SA