Graduate School of Mathematical Sciences, The University of Tokyo
Journal of Mathematical Sciences, The University of Tokyo. Vol. 4 (1997), No. 2, Page 373-383
In this paper we consider the conjecture of Gross on the special values of abelian $L$-functions when the Galois group $G$ is an elementary abelian $l$-group. Under some restrictions, we prove that the conjecture holds when the class number of the base field is prime to $l$.