Ref HAL: hal-01334181_v1
Ref Arxiv: 1606.05495
DOI: 10.1007/s00029-018-0444-9
WoS: WOS:000449794800003
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
7 Citations
Résumé:

Theta series for lattices with indefinite signature $(n_+,n_-)$ arise in many areas of mathematics including representation theory and enumerative algebraic geometry. Their modular properties are well understood in the Lorentzian case ($n_+=1$), but have remained obscure when $n_+\geq 2$. Using a higher-dimensional generalization of the usual (complementary) error function, discovered in an independent physics project, we construct the modular completion of a class of `conformal' holomorphic theta series ($n_+=2$). As an application, we determine the modular properties of a generalized Appell-Lerch sum attached to the lattice ${\operatorname A}_2$, which arose in the study of rank 3 vector bundles on $\mathbb{P}^2$. The extension of our method to $n_+>2$ is outlined.

Commentaires: 30 pages, 2 figures