✦ LIBER ✦

Power Sums over Finite Subspaces of a Field

✍ Scribed by Nigel P. Byott; Robin J. Chapman

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 134 KB
Volume: 5
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.1999.0243

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✦ Synopsis

Let < be a "nite additive subgroup of a "eld K of characteristic p'0. We consider sums of the form S F (< : )" TZ4 (v# )F for h50 and 3 K. In particular, we give necessary and su$cient conditions for the vanishing of S F (<; ), in terms of the digit sum in the base-p expansion of h, in the case that < has index p in K. The proof involves the polynomial f 4 (x)" TZ4 (x!v). We de"ne <R"f 4 (K). In the case that K is "nite, the polynomial f <R can be viewed as a generalised trace Tr 4 : KP< which coincides with the usual trace if < is a sub"eld of K.

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