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In this article, we study special values of the Dedekind zeta function overan imaginary quadratic field. The values of the Dedekind zeta function at anyeven integer over any totally real number field is quite well known inliterature. In fact, in one of the famous article, Zagier obtained an explicitformula for Dedekind zeta function at point 2 and conjectured an identity atany even values over any number field. We here exhibit the identities for botheven and odd values of the Dedekind zeta function over an imaginary quadraticfield which are analogous to Ramanujan's identities for even and odd zetavalues over $\Q$. Moreover, any complex zeta values over imaginary quadraticfield may also be evaluated from our identities.

Explicit identities on zeta values over imaginary quadratic field