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On the Lacunarity of Two-Eta-Products

On the Lacunarity of Two-Eta-Products Abstract We classify all lacunary modular forms corresponding to the two-eta-products η 𝑟 (𝑧) η 𝑠 (𝑚𝑧) for 𝑚 = 3, 4, 5, where 𝑟 + 𝑠 is even and 𝑟𝑠 ≠ 0. We show that there are no lacunary non-cusp forms corresponding to the eta-product η 𝑟 (𝑧) η 𝑠 (𝑚𝑧), 𝑚 ≥ 4. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

On the Lacunarity of Two-Eta-Products

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References (9)

Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2006.659
Publisher site
See Article on Publisher Site

Abstract

Abstract We classify all lacunary modular forms corresponding to the two-eta-products η 𝑟 (𝑧) η 𝑠 (𝑚𝑧) for 𝑚 = 3, 4, 5, where 𝑟 + 𝑠 is even and 𝑟𝑠 ≠ 0. We show that there are no lacunary non-cusp forms corresponding to the eta-product η 𝑟 (𝑧) η 𝑠 (𝑚𝑧), 𝑚 ≥ 4.

Journal

Georgian Mathematical Journal – de Gruyter

Published: Dec 1, 2006

Keywords: Dedekind eta-function; lacunary forms; Hecke forms; modular forms

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