论文信息 - Factorization in Fq(x) and Brownian Motion

Factorization in Fq(x) and Brownian Motion

We consider the set of polynomials of degree n over a finite field and put the uniform probability measure on this set. Any such polynomial factors uniquely into a product of its irreducible factors. To each polynomial we associate a step function on the interval [0,1] such that the size of each jump corresponds to the number of factors of a certain degree in the factorization of the random polynomial. We normalize these random functions and show that the resulting random process converges weakly to Brownian motion as n→∞. This result complements earlier work by the author on the order statistics of the degree sequence of the factors of a random polynomial. This research was partially supported by NSF grant DMS90 099074. 1

Jennie C. Hansen

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