Skip to main content

Research Repository

Advanced Search

On some incomplete theta integrals

Funke, Jens; Kudla, Stephen

On some incomplete theta integrals Thumbnail


Stephen Kudla


In this paper we construct indefinite theta series for lattices of arbitrary signature as ‘incomplete’ theta integrals, that is, by integrating the theta forms constructed by the second author with J. Millson over certain singular -chains in the associated symmetric space . These chains typically do not descend to homology classes in arithmetic quotients of , 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.


Funke, J., & Kudla, S. (2019). On some incomplete theta integrals. Compositio Mathematica, 155(9), 1711-1746.

Journal Article Type Article
Acceptance Date Apr 2, 2019
Online Publication Date Aug 2, 2019
Publication Date Sep 30, 2019
Deposit Date May 1, 2019
Publicly Available Date Feb 2, 2020
Journal Compositio Mathematica
Print ISSN 0010-437X
Electronic ISSN 1570-5846
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 155
Issue 9
Pages 1711-1746


Accepted Journal Article (469 Kb)

Copyright Statement
This article has been published in a revised form in Compositio Mathematica This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © The Authors 2019.

You might also like

Downloadable Citations