$p$-th power relations and Euler-Carlitz relations among multizeta values (Algebraic Number Theory and Related Topics 2013)

Abstract

In this paper, we study p-th power relations and Euler-Carlitz relations among multizeta values in characteristic p. By definition, two multizeta values have the p-th power relation if their indices map to each other multiplying by some power of p. The multizeta values of depth one at even integers satisfy Euler-Carlitz relations which are analogues of the relations among the Riemann zeta values at positive even integers. We prove that all algebraic relations among given multizeta values come from p-th power relations and Euler-Carlitz relations if their indices satisfy some conditions.