Vol. 65, No. 1, 1976

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Gauss sums and integral quadratic forms over local fields of characteristic 2

Delores Arletta Williams

Vol. 65 (1976), No. 1, 271–283

The theory of Gauss sums is developed for integral quadratic forms over a local field of characteristic 2, and Gauss sums are used to characterize these forms. For a character χ and an integral lattice L, the Gauss sum χ(L) is either zero, a nonnegative power of two, or the negative of a positive power of two. Gauss sums alone characterize the integral equivalence classes for modular lattices. For arbitrary lattices, other invariants are required.

Mathematical Subject Classification
Primary: 10C05, 10C05
Received: 30 December 1975
Revised: 18 February 1976
Published: 1 July 1976
Delores Arletta Williams