q-multiple zeta values at roots of unity associated with q-(r,s)-Stirling numbers

The study on multiple zeta values has been actively studied since the 1990s. Several different types of (generalized) multiple zeta functions have been introduced and studied by many researchers. 

In this talk, we introduce a q-generalization of finite version of multiple zeta values. Many relations have been established by several researchers. But, we are interested in explicit formulas at roots of unity, where we can see the forms of polynomials with rational numbers.  On the other hand, the classical Stirling numbers (of the first kind and of the second kind) have been widely studied and generalized in various fields, in particular, in combinatorics. In this talk, we show how certain kinds of generalized Stirling number are closely connected with finite version of multiple zeta values.