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Effective counting for discrete lattice orbits in the plane via Eisenstein series by Burrin, Claire; Nevo, Amos; Rühr, Rene; Weiss, Barak is a scholarly article available to read on EtoBox.

What is Effective counting for discrete lattice orbits in the plane via Eisenstein series about?

We prove effective bounds on the rate in the quadratic growth asymptotics for the orbit of a non-uniform lattice of SL(2,R), acting linearly on the plane. This gives an error bound in the count of saddle connection holonomies, for some Veech surfaces. The proof uses Eisenstein series and relies on earlier work of many authors (notably Selberg). Our results improve earlier error bounds for counting in sectors and in smooth star shaped domains.

Author

Burrin, Claire; Nevo, Amos; Rühr, Rene; Weiss, Barak

Published

2019

Language

EN