Duality in Tails of Multiple-zeta values
by
O-Yeat Chan
Department of Mathematics, Dalhousie University
Coauthors: Jonathan M. Borwein

Multiple zeta-values (MZVs), or Euler-Zagier sums, are higher dimensional analogues of the Riemann zeta function. They are defined by a sum over a k-dimensional simplex:

z(a1, ..., ak) : = å n1 > n2 > ... > nk > 0  k Õ i=1  1 niai .

Connection formulas between an MZV and other MZVs of lower dimension, also known as reduction formulas, are analytically, combinatorially, and computationally interesting. One fundamental reduction formula is the MZV duality formula. In this talk, we will give a generalization of MZV duality to the tails of MZVs, using elementary methods.

Date received: June 8, 2008