Applications of shuffle product to restricted decomposition formulas for multiple zeta values

Shuffle product formulas of multiple zeta values

“…When a, b 1 1, applying the map ζ to the formula (3.3), we get the formula for the product of the form ζ(m, {1} n )ζ(m 1 , {1} n1 , m 2 , {1} n2 ). The formula obtained here looks different from that in [13,Theorem 1.3]. We show in Appendix B that these two formulas are essentially identical.…”

“…The formula of x a y r X x b y s . In this subsection, we consider the shuffle product of multiple zeta values of the form ζ(m, {1} n ), which had been studied in [5,13].…”

“…And this result was generalized to the product of n multiple zeta values with one string of 1's in [4,Main Theorem], which also generalized the formula of the products of n Riemann zeta values in [3,Theorem 1.2]. By an algebraic method, P. Lie, L. Guo and B. Ma also gave a shuffle product formula of two multiple zeta values with one string of 1's, and obtained a formula of the product of two multiple zeta values one of which with two strings of 1's in [13,Theorem 1.1,Theorem 1.3].…”

Stuffle Product Formulas of Multiple Zeta Values

“…During the study of multiple zeta values, several shuffle product formulas were found. For example, as generalizations of Euler's decomposition formula, Eie and Wei essentially studied the shuffle product z k z m 1 X z l z n 1 in [2], Lei, Guo and Ma obtained the formula for shuffle product z k z m 1 X z l1 z n1 1 z l2 z n2 1 in [4], and we studied the shuffle products of words with more strings of z 1 's in [5]. For the stuffle product, Chen obtained a formula for the product z k z m p * z l z n p in [1].…”

Applications of stuffle product of multiple zeta values

“…Recently, Eie, Wei [5] and Lei, Guo, Ma [8] are both based on the shuffle product to get some restricted decomposition formulas for MZVs. For example, [8].)…”