Vol. 15, No. 3, 1965

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Integral invariants for vectors over local fields

Donald Gordon James

Vol. 15 (1965), No. 3, 905–916

This paper considers isometric invariants of vectors in lattices (quadratic forms) over the ring of integers in a local field for the prime 2. By extending the notion of order to vectors in the lattice we obtain a set of invariants which enable the general vector to be decomposed into a sum of simple vectors. The lengths of these simple vectors are invariant modulo certain powers of 2 and these lengths together with the original invariants form a complete set for the 2-adic integers. In the special case where there are no one dimensional, orthogonal sublattices (improper quadratic forms) the invariants form a complete set for all local fields.

Mathematical Subject Classification
Primary: 10.16
Received: 20 August 1964
Published: 1 September 1965
Donald Gordon James