http://swrc.ontoware.org/ontology#UnrefereedArticle
Gross'Conjecture for Extensions Ramified over Three Points of $\Bbb P^1$
en
Reid Michael
B. Gross has formulated a conjectural generalization of the class number formula. Suppose $L/K$ is an abelian extension of global fields with Galois group $G$. A generalized Stickelberger element $θ \in \ZZ[G]$ is constructed from special values of $L$-functions at $s = 0$. Gross'conjecture then predicts some $I$-adic information about $θ$, where $I \subseteq \ZZ[G]$ is the augmentation ideal. In this paper, we prove (under a mild hypothesis) the conjecture for the maximal abelian extension of the rational function field $\FF_q(X)$ that is unramified outside a set of three degree $1$ places.
Journal of mathematical sciences, the University of Tokyo
10
1
119-138
2003
13405705
AA11021653
415
Graduate School of Mathematical Sciences, The University of Tokyo