TWO ZAGIER-LIFTS

Abstract

Zagier lift gives a relation between weakly holomorphic modular functions and weakly holomorphic modular forms of weight 3=2. Duke and Jenkins extended Zagier-lifts for weakly holomorphic modular forms of negative-integral weights and recently Bringmann, Guerzhoy and Kane extended them further to certain harmonic weak Maass forms of negative-integral weights. New Zagier-lifts for harmonic weak Maass forms and their relation with BringmannGuerzhoy-Kane's lifts were discussed earlier. In this paper, we give explicit relations between the two different lifts via direct computation.

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