# Bounding hyperbolic and spherical coefficients of Maass forms

@article{Blomer2014BoundingHA, title={Bounding hyperbolic and spherical coefficients of Maass forms}, author={Valentin Blomer and Farrell Brumley and Alex Kontorovich and Nicolas Templier}, journal={Journal de Theorie des Nombres de Bordeaux}, year={2014}, volume={26}, pages={559-578} }

We develop a new method to bound the hyperbolic and spherical Fourier coefficients of Maass forms defined with respect to arbitrary uniform lattices. Let Σ be a compact hyperbolic surface, endowed with a metric of constant negative curvature −1. Let f be a non-constant eigenfunction of the Laplacian (∆ + λ)f = 0 on Σ, normalized so that ||f ||2 = 1. Let C be a closed geodesic or a geodesic circle in Σ. (By a geodesic circle we mean the set of points of fixed positive distance from a given point…

## 3 Citations

### Lattice points counting and bounds on periods of Maass forms

- MathematicsTransactions of the American Mathematical Society
- 2019

We provide a "soft" proof for non-trivial bounds on spherical, hyperbolic and unipotent Fourier coefficients of a fixed Maass form for a general co-finite lattice $\Gamma$ in $PGL(2,R)$. We use the…

### Effective equidistribution of shears and applications

- Mathematics
- 2015

A “shear” is a unipotent translate of a cuspidal geodesic ray in the quotient of the hyperbolic plane by a non-uniform discrete subgroup of $${\text {PSL}}(2,\mathbb {R})$$PSL(2,R), possibly of…

### Effective equidistribution of shears and applications

- MathematicsMathematische Annalen
- 2017

A “shear” is a unipotent translate of a cuspidal geodesic ray in the quotient of the hyperbolic plane by a non-uniform discrete subgroup of PSL(2,R)\documentclass[12pt]{minimal} \usepackage{amsmath}…

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