MA thesis available - University of Hawaii
MA thesis available - University of Hawaii
MA thesis available - University of Hawaii
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16 M. CHI<br />
We now prove that in Proposition 3, in fact, γ = 0.<br />
Proposition 5. There exists a weak harmonic Maass form M <strong>of</strong> weight zero on Γ0(32) such<br />
that<br />
E4(4τ)<br />
η(4τ) 2 = D(M).<br />
η(8τ) 2<br />
Pro<strong>of</strong>. We write the Fourier expansion <strong>of</strong> M = M + + M − as<br />
M + = <br />
a(n)q n , M − = <br />
We thus have that<br />
n≫−∞<br />
tg = ξ(M) = −4π <br />
n≥1<br />
n