A sparse equidistribution problem for expanding horocycles on the modular surface

Abstract: The orbits of the horocycle flow on hyperbolic surfaces (or orbifolds) are classified: each orbit is either dense or a closed horocycle around a cusp. Expanding closed horocycles are themselves asymptotically dense, and in fact become equidistributed on the surface. The precise rate of equidistribution is of interest; on the modular surface, Zagier observed that a particular rate is equivalent to the Riemann hypothesis being true. In this talk, I will discuss the asymptotic behavior of evenly spaced points along an expanding closed horocycle on the modular surface. In this problem, the number of points depends on the expansion rate of the horocycle, and the difficulty is that these points are no more invariant under the horocycle flow. This is based on joint work with Uri Shapira and Shucheng Yu.

number theory

Audience: researchers in the topic

Heilbronn number theory seminar

Series comments: This is part of the University of Bristol's Heilbronn number theory seminar. If you wish to attend the talk (and are not a Bristolian), please register using this form or email us at bristolhnts@gmail.com with your name and affiliation (if any).

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