2020/01/21 by Cornelia Druţu, Druţu, Cornelia, Norbert Peyerimhoff +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Point processes and geometric inequalities #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2001.07693
openalex publication_date 2020/01/21 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We use a dictionary between lattice point counting inside dilated d-dimensional ellipsoids (Euclidean counting) and counting of lifts of a closed horosphere that intersect a ball of increasing radius, to obtain two types of results. Firstly, via an L2-integral error estimate for Euclidean counting, we prove effective equidistribution results for a family of expanding horospheres in the locally symmetric space SO(d) SL(d,R) / SL(d,Z). Secondly, we derive from uniform error estimates in Euclidean counting, error terms for counting SL(d,Z)-orbit points in a certain increasing family of subsets in SO(d) SL(d,R) (which we call truncated chimneys), and for counting the number of lifts of a closed horosphere that intersect a ball with large radius.