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 Eisenstein in 1848,[1] named "Eisenstein sums" by Stickelberger in 1890,[2] and rediscovered by Yamamoto in 1985,[3] 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.[4]