A note on exponential sums

L. Carlitz

Vol. 30 (1969), No. 1, 35–37

DOI: 10.2140/pjm.1969.30.35

Abstract

Put S(a) = Σ_x,y≠0e(x + y + ax¹y¹), where xx¹ = yy¹ = 1, e(x) = x + x² + ⋯ + x^2n−l and the summation is over all nonzero x,y in the finite field GF(q),q = 2ⁿ. Then it is shown that S(a) = 0(q) for all a ∈ GF(a).

Mathematical Subject Classification

Primary: 10.41

Milestones

Received: 17 June 1968

Published: 1 July 1969