Alladi Ramakrishnan Hall

Special values of Dedekind zeta function for abelian number fields

Dhananjaya Sahu

IMSc

Let $\K$ be a totally imaginary abelian number field and let $\K^+$ be the the maximal totally real subfield of $\K$. We will report on some new work about the nature of $\frac{\zeta_{\K}(s)}{\zeta_{\K^+}(s)}$ at odd positive integers. We will also discuss the nature of $\zeta_{\K}(s)$ at even positive integers, when $\K$ is a totally real abelian number field.