2020-01-19T22:20:12Zhttps://repository.dl.itc.u-tokyo.ac.jp/?action=repository_oaipmhoai:repository.dl.itc.u-tokyo.ac.jp:000403652019-12-24T07:27:15Z00312:06865:07071:0707500009:00504:06868:07073:07076
On the special values of abelian L-functionsenghttp://hdl.handle.net/2261/1584Departmental Bulletin PaperTan, Ki-SengHere 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 Tokyo12305319199413405705AA11021653application/pdf415https://repository.dl.itc.u-tokyo.ac.jp/?action=repository_action_common_download&item_id=40365&item_no=1&attribute_id=19&file_no=1Graduate School of Mathematical Sciences, The University of Tokyo2017-06-14