Moment estimates for squarefree integers on short intervals
Moment estimates for squarefree integers on short intervals

Maria Avdeeva, Princeton University
Fine Hall 601
Squarefree integers are known to have asymptotic density 6/(pi^2). Fix some x and let n be distributed uniformly on the integers between 1 and x. Consider the corresponding variance of the number of squarefree integers on a short interval [n+1, n+N] and let x tend to infinity. In 1982, R.Hall proved that the limiting variance behaves asymptotically, as N tends to infinity, like C*N^{1/2} for some constant C. In 1987, Hall also derived some estimates for higher moments of this random variable. Following another method, we will obtain a different estimate for the third moment. If time permits, we will also discuss higher moments and generalization of Hall's result to the case of kfree integers.