The standard way of representing numbers on computers gives rise to errors
which increase as computations progress. Using p-adic valuations can reduce
error accumulation. Valuation theory tells us that p-adic and standard valuations
cannot be directly compared. The p-adic valuation can, however, be used in
an indirect way. This gives...
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...