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Evaluation of some exponential sums over a finite field

✍ Scribed by L. Carlitz

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
525 KB
Volume
96
Category
Article
ISSN
0025-584X

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✦ Synopsis

Evaluation of some exponential sums over i l finite field By L. CAF~LITZ of Durham (U.S.A.) (Eingegangen am 10.7.1978) 1. Introduction. Let Fq = QF(q) denote the finite field of order q = p", p prime, n 2 1. For a E Fq put t(a) = a + up + + up"-' and e(a) = p i W / p , so that t(aP) = t(a), e(aP) = e(a), The exponential sum S(a, b) is defined by

For p = 2 the writer [l] has evaluated S(a, a). The cases n even and n odd require separate treatment. In particular, for n = 2m, a E F , a +-0, it it3 proved that according as a is or is not a cube in F. For the general case, if a = c3, c E P, then according as

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