Loading...
Please wait, while we are loading the content...
Similar Documents
On some incomplete theta integrals
| Content Provider | Scilit |
|---|---|
| Author | Funke, Jens Kudla, Stephen |
| Copyright Year | 2019 |
| Description | Journal: Compositio Mathematica In this paper we construct indefinite theta series for lattices of arbitrary signature $(p,q)$ as ‘incomplete’ theta integrals, that is, by integrating the theta forms constructed by the second author with J. Millson over certain singular $q$ -chains in the associated symmetric space $D$ . These chains typically do not descend to homology classes in arithmetic quotients of $D$ , and consequently the theta integrals do not give rise to holomorphic modular forms, but rather to the non-holomorphic completions of certain mock modular forms. In this way we provide a general geometric framework for the indefinite theta series constructed by Zwegers and more recently by Alexandrov, Banerjee, Manschot, and Pioline, Nazaroglu, and Raum. In particular, the coefficients of the mock modular forms are identified with intersection numbers. |
| Ending Page | 1746 |
| Starting Page | 1711 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x19007504 |
| Journal | Compositio Mathematica |
| Issue Number | 9 |
| Volume Number | 155 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2019-09-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Applied Mathematics Theta Integrals Construct Indefinite Theta Series |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
