On the convergence of certain indefinite theta series
Volume 215 / 2024
Acta Arithmetica 215 (2024), 309-325
MSC: Primary 11F03; Secondary 11F27
DOI: 10.4064/aa230418-10-3
Published online: 21 August 2024
Abstract
We study certain indefinite theta series associated to a finite set of vectors in an inner product space of signature $(n,2)$. In particular, under certain incidence conditions, we show in an elementary way the convergence of these theta series, thus proving a conjecture of Alexandrov, Banerjee, Manschot and Pioline. Moreover, we show that these conditions are necessary for the convergence.
