Vol. 80, No. 2, 1979

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A Witt’s theorem for unimodular lattices

Y. C. Lee

Vol. 80 (1979), No. 2, 509–516

Let K be a dyadic local field, o its ring of integers, L a regular unimodular lattice over o. If x and y are vectors in L, we ask for necessary and sufficient conditions to map x isometrically to y. Trojan and James obtain conditions via a T-invariant when o is 2-adic. Hsia uses characteristic sets and G-invariants for vectors and he solves the problem when o is dyadic in general. We define here a new numerical invariant, the degree of a vector, which reflects more on the structure of L and the relationship between x, y and L. The Witt conditions will be stated in terms of this degree invariant.

Mathematical Subject Classification 2000
Primary: 10C05, 10C05
Secondary: 06C99, 15A63
Received: 31 August 1977
Published: 1 February 1979
Y. C. Lee