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Speaker:
Claire Burrin
Affiliation:
ETH Zürich
Date:
Wed, 26/04/2023 - 11:30 - 12:30
Location:
MPIM Lecture Hall In joint work with Flemming von Essen, we use modular forms to construct a function that measures the winding of closed geodesics about a prescribed cusp of a hyperbolic surface. On the modular surface, this winding number is given by the Rademacher function $\psi$, which is a conjugacy class invariant on the modular group, arises from the study of the multiplier system of Dedekind’s eta function, and computes hyperbolic periods of Hecke’s weight 2 Eisenstein series. We obtain the following Dirichlet-type equidistribution theorem for various families of surfaces: Given a set $A$ of integers with natural density $d(A)$, the set of prime geodesics with winding number in $A$ has density $1/d$.
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