Title: Generalized hypergeometric series allied to moments in the four-step uniform random walk problem
Authors: Roderick McCrorie - University of St Andrews (United Kingdom) [presenting]
Abstract: The focus is on the representation of odd moments of the distribution of a four-step random walk in even dimensions, which are based on a mathematical constant representable in terms of the integral over the unit interval of the square of the complete elliptic integral of the first kind. New symmetries in critical values of the L-series of two underlying cusp forms are established, unblocking the problem of representing the constant in terms of very well-poised generalized hypergeometric series and revealing it has a formal counterpart. Both the constant and its counterpart are seen already to play significant roles in multidisciplinary contexts. A connection is made to the open econometric problem of fully characterizing the bias in the canonical autoregressive model under the unit root hypothesis, which shares similar features.