The hyperbolic lattice point problem in conjugacy classes

Abstract

For $\Gamma$ a cocompact or cofinite Fuchsian group, we study the hyperbolic lattice point problem in conjugacy classes, which is a modification of the classical hyperbolic lattice point problem. We use large sieve inequalities for the Riemann surfaces $\Gamma \backslash \mathbb{H}$ to obtain average results for the error term, which are conjecturally optimal. We give a new proof of the error bound $O(X^{2/3})$, due to A. Good. For $SL(2,\mathbb{Z})$ we interpret our results in terms of indefinite quadratic forms.

arXiv commentFInal version of arXiv:1504.01307 to appear in Forum Math