Shuffle Product Formulas of Multiple Zeta Values
نویسنده
چکیده
Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two multiple zeta values, some restricted shuffle product formulas of the product of two multiple zeta values, and a restricted shuffle product formula of the product of n multiple zeta values.
منابع مشابه
Explicit Double Shuffle Relations and a Generalization of Euler’s Decomposition Formula
We give an explicit formula for the shuffle relation in a general double shuffle framework that specializes to double shuffle relations of multiple zeta values and multiple polylogarithms. As an application, we generalize the well-known decomposition formula of Euler that expresses the product of two Riemann zeta values as a sum of double zeta values to a formula that expresses the product of t...
متن کاملA New Shuffle Convolution for Multiple Zeta Values
Recently, interest in shuffle algebra has been renewed due to their connections with multiple zeta values. In this paper, we prove a new shuffle convolution that implies a reduction formula for the multiple zeta value ζ ({5, 1}n).
متن کاملHigher Order Shuffle Regularization for Multiple Zeta Values
We study the higher order shuffle regularization for multiple zeta values and define higher order regularized shuffle relations. We find that higher order regularized shuffle relations can be deduced from the group-like property of the Drinfel’d associator.
متن کاملMultiple Polylogarithms: A Brief Survey
We survey various results and conjectures concerning multiple polylogarithms and the multiple zeta function. Among the results, we announce our resolution of several conjectures on multiple zeta values. We also provide a new integral representation for the general multiple polylogarithm, and develop a q-analogue of the shuffle product.
متن کاملDouble Shuffle Relations of Euler Sums
Abstract. In this paper we shall develop a theory of (extended) double shuffle relations of Euler sums which generalizes that of multiple zeta values (see Ihara, Kaneko and Zagier, Derivation and double shuffle relations for multiple zeta values. Compos. Math. 142 (2)(2006), 307–338). After setting up the general framework we provide some numerical evidence for our two main conjectures. At the ...
متن کامل