In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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, named "Eisenstein sums" by Stickelberger in 1890, and rediscovered by Yamamoto in 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''.
References
Bibliography
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*{{Citation , last1=Yamamoto , first1=K. , title=Number theory and combinatorics. Japan 1984 (Tokyo, Okayama and Kyoto, 1984) , publisher=World Sci. Publishing , location=Singapore , mr=827799 , zbl=0634.12017 , year=1985 , chapter=On congruences arising from relative Gauss sums , pages=423–446
Algebraic number theory