REVIEW 1 cited by
Theta integrals and generalized error functions, II
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
Theta series for indefinite quadratic lattices were introduced by Zwegers, for signature (m-1,1), Alexandrov, Banerjee, Manschot and Pioline, for signature (m-2,2), and Nazaroglu, for signature (m-q,q). These series are modular modular completions, defined by means of generalized error functions, of certain non-modular holomorphic generating series associated to lattice vectors in positive cones. We show that these modular forms arise as integrals of the theta forms, defined in work of Millson and the second author, over certain singular q-cubes. We also give an explicit formula for the integrals of such forms over singular q-simplices. The sign function occurring in the holomorphic generating series arises as in intersection number of the singular q-cube or q-simplex with a totally geodesic subsymmetric space of codimension q. The cubical case for q=2 was treated in [11].
Forward citations
Cited by 1 Pith paper
-
Mock modularity of Calabi-Yau threefolds
The paper constructs explicit indefinite theta series solving the modular anomaly for rank 0 DT invariants, fixing these generating functions up to modular forms determined by polar terms.
Discussion (0). Continue with ORCID to comment.