## Local mixing on abelian covers of hyperbolic surfaces with cusps

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## Abstract:

We prove the local mixing theorem for geodesic flows on abelian covers of finite volume hyperbolic surfaces with cusps, which is a continuation of the work [Hee Oh and Wenyu Pan, Int. Math. Res. Not. 19 (2019), pp. 6036–6088]. We also describe applications to counting problems and the prime geodesic theorem.## References

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## Additional Information

**Wenyu Pan**- Affiliation: Pennsylvania State University, State College, Pennsylvania 16802
- Address at time of publication: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
- MR Author ID: 1207609
- Email: wup60@psu.edu, wenyu@math.uchicago.edu
- Received by editor(s): September 16, 2018
- Received by editor(s) in revised form: July 26, 2020, and September 8, 2020
- Published electronically: March 22, 2021
- Communicated by: Nimish Shah
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**149**(2021), 2501-2514 - MSC (2020): Primary 37A17
- DOI: https://doi.org/10.1090/proc/15340
- MathSciNet review: 4246801