On some free algebras of orthogonal modular forms

Wang, Haowu; Williams, Brandon

doi:10.1016/j.aim.2020.107332

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On some free algebras of orthogonal modular forms

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Wang, Haowu
Max Planck Institute for Mathematics, Max Planck Society;

External Ressource

https://doi.org/10.1016/j.aim.2020.107332
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arXiv:2003.05374.pdf
(Preprint), 234KB

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Citation

Wang, H., & Williams, B. (2020). On some free algebras of orthogonal modular forms. Advances in Mathematics, 373: 107332. doi:10.1016/j.aim.2020.107332.

Cite as: http://hdl.handle.net/21.11116/0000-0006-E3ED-F

Abstract

For 25 orthogonal groups of signature $(2,n)$ related to the root lattices $A_1$, $2A_1$, $3A_1$, $4A_1$, $A_2$, $A_3$, $A_4$, $A_5$, $A_6$, $A_7$, $D_4$, $D_5$, $D_6$, $D_7$, $D_8$, $E_6$, $E_7$, we prove that the algebras of modular forms on symmetric domains of type IV are freely generated by the additive lifts of some special Jacobi forms. The proof is universal and elementary.