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Measure-equivalence of quadratic forms

This paper examines the probability that a random polynomial of specific degree over a field has a specific number of distinct roots in that field. Probabilities are found for random quadratic polynomials with respect to various probability measures on the real numbers and p-adic numbers. In the process, some properties of the p-adic integer uniform random variable are explored. The measure Witt ring, a generalization of the canonical Witt ring, is introduced as a way to link quadratic forms and measures, and examples are found for various fields and measures. Special properties of the Haar measure in connection with the measure Witt ring are explored. Higher-degree polynomials are explored with the aid of numerical methods, and some conjectures are made regarding higher-degree p-adic polynomials. Other open questions about measure Witt rings are stated. / Graduation date: 1999

Identiferoai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/16319
Date07 May 1999
CreatorsLimmer, Douglas J.
ContributorsRobson, Robert O.
Source SetsOregon State University
Languageen_US
Detected LanguageEnglish
TypeThesis/Dissertation

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