# 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}
}
• Published 2014
• Mathematics
• Journal de Theorie des Nombres de Bordeaux
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
• Mathematics
Transactions 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
• 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
• Mathematics
Mathematische 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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