## Algebra of Borcherds products

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- by Shouhei Ma PDF
- Trans. Amer. Math. Soc.
**375**(2022), 4285-4305 Request permission

## Abstract:

Borcherds lift for an even lattice of signature $(p, q)$ is a lifting from weakly holomorphic modular forms of weight $(p-q)/2$ for the Weil representation. We introduce a new product operation on the space of such modular forms and develop a basic theory. The product makes this space a finitely generated filtered associative algebra, without unit element and noncommutative in general. This is functorial with respect to embedding of lattices by the quasi-pullback. Moreover, the rational space of modular forms with rational principal part is closed under this product. In some examples with $p=2$, the multiplicative group of Borcherds products of integral weight forms a subring.## References

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## Additional Information

**Shouhei Ma**- Affiliation: Department of Mathematics, Tokyo Institute of Technology, Tokyo 152-8551, Japan
- MR Author ID: 833420
- ORCID: 0000-0003-0707-6254
- Email: ma@math.titech.ac.jp
- Received by editor(s): July 24, 2021
- Received by editor(s) in revised form: October 12, 2021
- Published electronically: January 7, 2022
- Additional Notes: The author was supported by JSPS KAKENHI 17K14158, 20H00112, 21H00971
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**375**(2022), 4285-4305 - MSC (2020): Primary 11F37, 16S99, 11F27, 11F55, 11F50
- DOI: https://doi.org/10.1090/tran/8585
- MathSciNet review: 4419059