Georgian Mathematical Journal 13 (2006), No. 4, 659--673
Copyright Heldermann Verlag 2006
On the Lacunarity of Two-Eta-Products
Shaun Cooper
Inst. Information Math. Sciences, Massey University, Private Bag 102 904, North Shore Mail Centre, Auckland, New Zealand
s.cooper@massey.ac.nz
Sanoli Gun
Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India
jhulan@mri.ernet.in
Balakrishnan Ramakrishnan
Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India
ramki@mri.ernet.in
[Abstract-pdf]
We classify all lacunary modular forms corresponding to the two-eta-products $\eta^r(z)\eta^s(mz)$ for $m=3,4,5$, where $r+s$ is even and $rs\not=0$. We show that there are no lacunary non-cusp forms corresponding to the eta-product $\eta^r(z)\eta^s(mz)$, $m\ge 4$.
Keywords: Dedekind eta function, lacunary forms, Hecke forms, modular forms.
MSC: 11F20; 11F11
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