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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 Bringmann-Guerzhoy-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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참고문헌 (9)
참고문헌 신청
K. Bringmann / 2014 / Shintani lifts and fractional derivatives for harmonic weak Maass forms / Adv. Math 255:641~671
J. H. Bruinier / 2004 / On two geometric theta lifts / Duke Math. J 125(1):45~90
W. Duke / 2008 / Integral traces of singular values of weak Maass form / Algebra and Number Theory 2(5):573~593
W. Duke / 2011 / Cycle integrals of the j-function and mock modular forms / Ann. Math 173(2):947~981
B. Gross / 1987 / Heegner points and derivatives of L-series, II / Math. Ann 278:497~562
J. H. Bruinier / 2004 / On two geometric theta lifts / Duke Math. J 125(1):45~90
W. Duke / 2008 / Integral traces of singular values of weak Maass form / Algebra and Number Theory 2(5):573~593
W. Duke / 2011 / Cycle integrals of the j-function and mock modular forms / Ann. Math 173(2):947~981
B. Gross / 1987 / Heegner points and derivatives of L-series, II / Math. Ann 278:497~562
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