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

A note on odd zeta values over any number field and Extended Eisenstein series