Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Algebra of Borcherds products
HTML articles powered by AMS MathViewer

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


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.
Similar Articles
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:
  • 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:
  • MathSciNet review: 4419059