The reckoning of certain quartic and octic Gauss sums

Berndt, Bruce C. ; Chowla, S. (1977) The reckoning of certain quartic and octic Gauss sums Glasgow Mathematical Journal, 18 (2). pp. 153-155. ISSN 0017-0895

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Related URL: http://dx.doi.org/10.1017/S0017089500003190

Abstract

In this brief note, we evaluate certain quartic and octic Gauss sums with the use of theorems on fourth and eighth power difference sets. We recall that a subset H of a finite (additive) abelian group G is said to be a difference set of G [5, p. 64] if for some fixed natural number λ, every nonzero element of G can be written as a difference of two elements of H fin exactly λ ways.

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