ALGEBRAIC INDEPENDENCE OF THE CARLITZ PERIOD AND THE POSITIVE CHARACTERISTIC MULTIZETA VALUES AT n AND (n, n).

Let k be the rational function field over the finite field of q elements and ... its fixed algebraic closure. In this paper, we study algebraic relations over ... among the fundamental period ... of the Carlitz module and the positive characteristic multizeta values ζ(n) and ζ(n, n) for an "odd" integer n, where we say that n is "odd" if q - 1 does not divide n. We prove that these three elements are either algebraically independent over ... or satisfy some simple relation over k. We also prove that if 2n is "odd", then these three elements are algebraically independent over .... [ABSTRACT FROM AUTHOR]