http://swrc.ontoware.org/ontology#UnrefereedArticle
On the special values of abelian L-functions
en
Tan Ki-Seng
Here we give a proof of the $p$-portion of a conjecture of Gross over the global function fields of characteristic $p$. In this case, the conjecture is in fact a refinement of the class number formula. Here the classic Dedekind Zeta function is generalized by a $p$-adic measure which interpolates the special values of abelian L-functions, and the regulator of the units group is generalized by a $p$-adic regulator. The L-functions are associated to the characters of the maximal abelian extension of the given global field unramified outside a finite set {$v_0, v_1, \dots, v_r,$} of places of the field. The case that $r=1$ has been proved by Hayes. Gross also proved some congruence of the formula.
Journal of mathematical sciences, the University of Tokyo
1
2
305-319
1994
13405705
AA11021653
application/pdf
415
Graduate School of Mathematical Sciences, The University of Tokyo