The algebra of multiple harmonic series

Abstract

Recently there has been much interest in multiple harmonic series ζ(i1,i2,...,ik) = ∑ n1>n2>⋯>nk≥1 1/ni11ni22 ⋯ nikk (which converge when the exponents i; are positive integers and i1 > 1), also known as multiple zeta values or Euler/Zagier sums. Starting with the noncommutative polynomial algebra Q.