Stefan De Wannemacker: Annihilating polynomials for quadratic forms and Stirling numbers of the second kind

Submission: 2005, Aug 3

We present a set of generators of the full annihilator ideal for the Witt ring of an arbitrary field of characteristic unequal to two satisfying a non-vanishing condition on the powers of the fundamental ideal in the torsion part of the Witt ring. This settles a conjecture of Ongenae and Van Geel. This result could only be proved by first obtaining a new lower bound on the 2-adic valuation of Stirling numbers of the second kind.

2000 Mathematics Subject Classification: 11B73, 11E04

Keywords and Phrases: Quadratic forms, Witt ring, Annihilating polynomials, Stirling numbers of the second kind

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