Weights of the mod $p$ kernel of the theta operators

Siegfried Boecherer; Toshiyuki Kikuta; Sho Takemori

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arXiv · 1606.06390

Weights of the mod $p$ kernel of the theta operators

Siegfried Boecherer·Toshiyuki Kikuta·Sho Takemori

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Abstract

We give some relations between the weights and the prime $p$ of elements of the mod $p$ kernel of the generalized theta operator $\Theta ^{[j]}$. In order to construct examples of the mod $p$ kernel of $\Theta ^{[j]}$ from any modular form, we introduce new operators $A^{(j)}(M)$ and show the modularity of $F|A^{(j)}(M)$ when $F$ is a modular form. Finally, we give some examples of the mod $p$ kernel of $\Theta ^{[j]}$ and the filtrations of some of them.

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Siegfried Boecherer, Toshiyuki Kikuta, Sho Takemori. 2016-06-21. Weights of the mod $p$ kernel of the theta operators. https://arxiv.org/abs/1606.06390

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