Keeping Secrets: The Case for a North American Trade Secret Agreement

In this paper, I attempt to give an overview of the statutory trade secret protections available in the United States, Canada, and Mexico, and suggest a solution to the problem of inadequate and confusing trade secret legislation: an international agreement between the NAFTA signatories criminalizing the theft of trade secrets

Squarefree polynomials and Mobius values in short intervals and arithmetic progressions

We calculate the mean and variance of sums of the M\"obius function and the indicator function of the squarefrees, in both short intervals and arithmetic progressions, in the context of the ring of polynomials over a finite field of $q$ elements, in the limit $q\to \infty$. We do this by relating the sums in question to certain matrix integrals over the unitary group, using recent equidistribution results due to N. Katz, and then by evaluating these integrals. In many cases our results mirror what is either known or conjectured for the corresponding problems involving sums over the integers, which have a long history. In some cases there are subtle and surprising differences. The ranges over which our results hold is significantly greater than those established for the corresponding problems in the number field setting.Comment: Added references and corrected misprint