A Weight-Depth Theorem for a Class of Multiple L-values

Research paper by David Terhune

Indexed on: 17 Mar '06Published on: 17 Mar '06Published in: Mathematics - Number Theory


An arbitrary-depth reduction theorem for the `convolution' multiple L-values of Euler-Zagier type is proven by an analytic method. To this end, generalized polylogarithms associated to Dirichlet characters are defined. The proof uses the monodromies of these functions and the parities of generating functions of generalized Bernoulli numbers. Some general formulas for resulting reductions in the depth 2 case are provided.