LEVEL TWO GENERALIZATION OF ARAKAWA-KANEKO ZETA FUNCTION AND POLY-COSECANT NUMBERS (Various aspects of multiple zeta values)

Abstract

We present a level two generalization of Arakawa-Kaneko zeta function introduced by T. Arakawa and M. Kaneko. We prove certain formulas for Arakawa-Kaneko zeta function of level two. Also, we study the level two generalization of poly-Bernoulli numbers, which is referred to as the poly-cosecant numbers. We obtain a recurrence and two explicit formulas for poly-cosecant numbers. Moreover, we extend those formulas for multiple versions in a similar manner. This is in part a joint work with M. Kaneko and H. Tsumura.