Effective counting for discrete lattice orbits in the plane via Eisenstein series

DOI10.4171/LEM/66-3/4-1zbMath1478.11062arXiv1905.01493MaRDI QIDQ2070047

Barak Weiss, Amos Nevo, Claire Burrin, Rene Rühr

Publication date: 21 January 2022

Published in: L'Enseignement Mathématique. 2e Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.01493

zbMATH Keywords

Eisenstein seriesVeech surfacesdiscrete lattice orbitseffective counting

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (2)

Fourier expansion of light‐cone Eisenstein series ⋮ Group actions and harmonic analysis in number theory. Abstracts from the workshop held May 7--12, 2023

Cites Work

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• Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow
• Local analysis of Selberg's trace formula
• Exponential mixing for the Teichmüller flow
• Teichmüller curves, triangle groups, and Lyapunov exponents
• Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
• The billiard in a regular polygon
• Siegel measures
• Density of integer points on affine homogeneous varieties
• Mixing, counting, and equidistribution in Lie groups
• Equidistribution of Kronecker sequences along closed horocycles
• Affine mappings of translation surfaces: Geometry and arithmetic
• Sup-norm bounds for Eisenstein series
• Hybrid subconvexity for class group \(L \)-functions and uniform sup norm bounds of Eisenstein series
• Effective counting on translation surfaces
• Schwarz triangle mappings and Teichmüller curves: The Veech-Ward-Bouw-Möller curves
• Asymptotic formulas on flat surfaces
• Counting lattice points
• On the statistics of the minimal solution of a linear Diophantine equation and uniform distribution of the real part of orbits in hyperbolic spaces
• Asymptotic behavior of periodic orbits of the horocycle flow and eisenstein series
• Planar structures and billiards in rational polygons: the Veech alternative
• Spectra of hyperbolic surfaces
• Primitive lattice points in convex planar domains
• Effective equidistribution of the real part of orbits on hyperbolic surfaces
• Grid Graphs and Lattice Surfaces

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