A combinatorial problem in finite fields. I

Gerald Ira Myerson

Vol. 82 (1979), No. 1, 179–187

DOI: 10.2140/pjm.1979.82.179

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