Eisenstein sum

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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.


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).