The special values of Dirichlet L-functions as an analogue of the Iwasawa power series

Abstract

For two different prime numbers p and l, the special values of Dirichlet L-functions in a finite field of characteristic p are considered as a function on the l-power roots of unity, which is an analogue of the Iwasawa power series. In this setting, we prove various properties of these functions, for example, transcendence and linear independence over rational functions, which are non-equal characteristic analogues of the results of Angles-Ranieri [Ann. Inst. Fourier (Grenoble) 60 (2010), no. 5, 1831-1855] and the author [Proc. Amer. Math. Soc. 138 (2010), no. 6, 1955-1963].