Vol. 82, No. 1, 1979

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A combinatorial problem in finite fields. I

Gerald Ira Myerson

Vol. 82 (1979), No. 1, 179–187
Abstract

Given a subgroup G of the multiplicative group of a finite field, we investigate the number of representations of an arbitrary field element as a sum of elements, one from each coset of G. When G is of small index, the theory of cyclotomy yields exact results. For all other G, we obtain good estimates.

This paper formed a portion of the author’s doctoral dissertation.

Mathematical Subject Classification 2000
Primary: 05A15
Secondary: 12C20
Milestones
Received: 1 April 1978
Published: 1 May 1979
Authors
Gerald Ira Myerson