Mock modular Eisenstein series with Nebentypus

By the theory of Eisenstein series, generating functions various divisor arise as modular forms. It is natural to ask whether further systematically in mock We establish, using method Zagier and Zwegers on holomorphic projection, that this indeed case for certain (twisted) “small divisors” summatory [Formula: see text]. More precisely, terms weight 2 quasimodular series text] a generic Shimura theta function text], we show there constant which half integral (polar) form. These include combinatorial objects such Andrews text]-function “consecutive parts” partition function. Finally, analogy with Serre’s result text]-adic form, these forms possess canonical congruences