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2013•arXiv (Cornell University)Open access

On the Lacunarity of some eta-products

Yudong Wang

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Abstract

The lacunarity is an interesting property of a formal series. We say a series is lacunary if "almost all" of its coefficients are zero. In this article we considered about the lacunarity of some eta-products like η(z)^2η(bz)^2, and proved that they are lacunary if and only if b is 1,2,3,4 or 16. Then We write them as linear combinations of some CM forms.

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The lacunarity is an interesting property of a formal series. We say a series is lacunary if "almost all" of its coefficients are zero. In this article we considered about the lacunarity of some eta-products like η(z)^2η(bz)^2, and proved that they are lacunary if and only if b is 1,2,3,4 or 16. Then We write them as linear combinations of some CM forms.

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Available abstract

The lacunarity is an interesting property of a formal series. We say a series is lacunary if "almost all" of its coefficients are zero. In this article we considered about the lacunarity of some eta-products like η(z)^2η(bz)^2, and proved that they are lacunary if and only if b is 1,2,3,4 or 16. Then We write them as linear combinations of some CM forms.

Key concepts: Lacunarity, Lacunary function, Mathematics, Series (stratigraphy), Property (philosophy), Pure mathematics, Fractal, Mathematical analysis

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