Abstract. Let U (n, n) be the rank n quasi-split unitary group over a number field. We show that the normalized Siegel Eisenstein series of U (n, n) has at most simple poles at the integers or half integers in certain strip of the complex plane.

AOn page 212 of his lost notebook, Ramanujan defined a new class invariant λ n and constructed a table of values for λ n . The paper constructs a new class of series for 1\π associated with λ n . The new method also yields a new proof of the Borweins' general series for 1\π belonging to Ramanujan's ' theory of q # '.

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