4 papers
Asymptotics and Sequential Closures of Continued Fractions and Generalizations
Douglas Bowman, James Mc Laughlin
Given a sequence of complex square matrices, , consider the sequence of their partial products, defined by . What can be said about the asymptotics as $n\to\…
The Algebra and Combinatorics of Shuffles and Multiple Zeta Values
Douglas Bowman, David M. Bradley
The algebraic and combinatorial theory of shuffles, introduced by Chen and Ree, is further developed and applied to the study of multiple zeta values. In particular, we establish e…
Multiple Polylogarithms: A Brief Survey
Douglas Bowman, David M. Bradley
We survey various results and conjectures concerning multiple polylogarithms and the multiple zeta function. Among the results, we announce our resolution of several conjectures on…
Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth
Douglas Bowman, David M. Bradley
We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-know…