@article{580d1a94ac854b3fa9d62f1ed80b6aa2,
title = "Bergman kernel asymptotics for singular metrics on punctured Riemann surfaces",
abstract = "We consider singular metrics on a punctured Riemann surface and on a line bundle, and study the behavior of the Bergman kernel in the neighborhood of the punctures. The results have an interpretation in terms of the asymptotic profile of the density-of-states function of the lowest Landau level in quantum Hall effect.",
keywords = "Bergman kernel function, Quantum Hall effect, Singular Hermitian metric",
author = "Dan Coman and Semyon Klevtsov and George Marinescu",
note = "Funding Information: Acknowledgements. The first author was partially supported by the National Science Foundation (grant nos. DMS-1300157 and DMS-1700011). The second author was partially supported by the German Excellence Initiative at the University of Cologne (grant nos. DFG-grant ZI513/2-1, NSh-1500.2014.2, RFBR 17-01-00585, and CRC/TR 183). The third author was partially supported by DFG funded project CRC/TRR 191 and gratefully acknowledges the support of Syracuse University, where part of this paper was written. Funding Information: Additional funding also came from the Institutional Strategy of the University of Cologne within the German Excellence Initiative. They gratefully acknowledge support from the Simons Center for Geometry and Physics, Stony Brook University, where some of the research for this paper was conducted. Publisher Copyright: Indiana University Mathematics Journal {\textcopyright}",
year = "2019",
doi = "10.1512/iumj.2019.68.7589",
language = "English (US)",
volume = "68",
pages = "593--628",
journal = "Indiana University Mathematics Journal",
issn = "0022-2518",
publisher = "Indiana University",
number = "2",
}