arXiv subjects
Publications and source records attributed to Pitu Sarkar.
In this paper, we obtain the meromorphic continuation of a q-analogue of multiple zeta function using an elementary formula called translation formula. We then obtain the matrix representation of the translation formula and using it, we locate the poles of the function and the corresponding residues. While locating the poles, we also obtain an inverse of an infinite triangular matrix in a particular case.
In this paper, we obtain a general t-shuffle product formula, using which we derive a generalized Euler decomposition formula for interpolated multiple zeta values. We also provide the same formula in case of height one through two different approaches: one by combinatorial description and another one by recursive formula.
In this paper, we obtain a restricted decomposition formula for interpolated multiple zeta values using t-stuffle product. We then derive a recursive formula of t-stuffle product, which also provides a route to the same formula. In both cases, combinatorial description of t-stuffle product is our basic tool. We also provide alternative proofs by mathematical induction for some of the results.
Shuffle algebra has been employed to give a proof of the duality theorem for multiple zeta-star values of height one.