Lattices with many Borcherds products. We prove that there are only finitely many isometry classes of even lattices ( L) of signature ( (2,n)) for which the space of cusp forms of weight ( 1+n/2) for the Weil representation of the discriminant group of ( L) is trivial. We compute the list of these lattices. They have the property that every Heegner divisor for the orthogonal group of ( L) can be realized as the divisor of a Borcherds product. We obtain similar classification results in greater generality for finite quadratic modules.
Keywords for this software
References in zbMATH (referenced in 8 articles , 1 standard article )
Showing results 1 to 8 of 8.
- Choi, Suh Hyun; Kim, Chang Heon; Kwon, Yeong-Wook; Lee, Kyu-Hwan: Rationality and (p)-adic properties of reduced forms of half-integral weight (2019)
- Opitz, Sebastian; Schwagenscheidt, Markus: Holomorphic Borcherds products of singular weight for simple lattices of arbitrary level (2019)
- Williams, Brandon: Poincaré square series of small weight (2019)
- Ma, Shouhei: On the Kodaira dimension of orthogonal modular varieties (2018)
- Opitz, Sebastian: Computation of Eisenstein series associated with discriminant forms (2018)
- Williams, Brandon: Vector-valued Hirzebruch-Zagier series and class number sums (2018)
- Bruinier, Jan Hendrik; Ehlen, Stephan; Freitag, Eberhard: Lattices with many Borcherds products (2016)
- Ehlen, Stephan: Singular moduli of higher level and special cycles (2015)