S. Barry Cooper, Sanoli Gun, Balakrishnan Ramakrishnan
Abstract
Abstract We classify all lacunary modular forms corresponding to the two-eta-products Ξ· π(π§)Ξ· π (ππ§) for π = 3, 4, 5, where π + π is even and ππ β 0. We show that there are no lacunary non-cusp forms corresponding to the eta-product Ξ· π(π§)Ξ· π (ππ§), π β₯ 4.
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Abstract We classify all lacunary modular forms corresponding to the two-eta-products Ξ· π(π§)Ξ· π (ππ§) for π = 3, 4, 5, where π + π is even and ππ β 0. We show that there are no lacunary non-cusp forms corresponding to the eta-product Ξ· π(π§)Ξ· π (ππ§), π β₯ 4.
Key concepts: Lacunary function, Lacunarity, Mathematics, Cusp (singularity), Product (mathematics), Pure mathematics, Modular form, Arithmetic