Multizeta shuffle relations for function fields with non rational infinite place

摘要

In contrast to the 'universal' multizeta shuffle relations, when the chosen infinite place of the function field over F-q, is rational, we show that in the non-rational case, only certain interesting shuffle relations survive, and the F-q-linear span of the multizeta values does not form an algebra. This is due to the subtle interactions between the larger finite field F-infinity, the residue field of the completion at infinity where the signs live and F-q, the field of constants where the coefficients live. We study the classification of these special relations which survive. (C) 2015 Elsevier Inc. All rights reserved.