  In this article, we have studied transformation formulas of zeta function at
odd integers over an arbitrary number field which in turn generalizes
Ramanujan's identity for the Riemann zeta function. The above transformation
leads to a new number field extension of Eisenstein series, which satisfies the
transformation $z \mapsto -1/z$ like an integral weight modular form over
SL$_2(\Z)$. The results provide number of important applications, which are
important in studying the behaviour of odd zeta values as well as Lambert
series in an arbitrary number field.
