CARMA ANALYSIS AND NUMBER THEORY SEMINAR Speaker: Dr James Wan, Singapore University of Technology and Design Title: Sums of Double Zeta Values Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 1:00 pm, Tue, 12th Jun 2012 Abstract: The double zeta values are one natural way to generalise the Riemann zeta function at the positive integers; they are defined by $\zeta(a,b) = \sum_{n=1}^\infty \sum_{m=1}^{n-1} 1/n^a/m^b$. We give a unified and completely elementary method to prove several sum formulae for the double zeta values. We also discuss an experimental method for discovering such formulae. Moreover, we use a reflection formula and recursions involving the Riemann zeta function to obtain new relations of closely related functions, such as the Witten zeta function, alternating double zeta values, and more generally, character sums. [Permanent link]