Indivisibility of special values of zeta functions associated to real quadratic fields

Abstract

We discuss some aspects of indivisibility of the special values of Dedekind zeta functions at negative odd integers associated to real quadratic fields. These values are closely related to the orders of certain cohomology groups and algebraic $\mathrm{K}$-groups.\n We show that, for an even number $n$ and a prime $p$ under some conditions, a quantitative result for the distribution of real quadratic fields whose special values of the $L$-functions at $1-n$ are indivisible by $p$.This research was partially supported by Grant-in-Aid for Young Scientists (B), 18740004, The Ministry of Education, Culture, Sports, Science and Technology, Japan