Title: p-adic asymptotic subalgebra enumeration

Abstract: Given a finite-dimensional p-adic algebra, we are interested in the number of subalgebras of index p^i as a function of i. To study this sequence of numbers we use a generating series, called the local subalgebra zeta function. Its poles describe the asymptotic growth of the number of subalgebras as i goes to infinity with the largest pole, in particular, dominating. From the p-adic perspective, however, it is the smallest pole which is most significant. This complementary point of view has allowed us to begin answering some central questions in the field of local zeta functions.