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Bounding hyperbolic and spherical coefficients of Maass forms

Valentin Blomer, Farrell Brumley, Alex Kontorovich, Nicolas Templier (2014)

Journal de Théorie 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.

Bounds on sup-norms of half-integral weight modular forms

Eren Mehmet Kıral (2014)

Acta Arithmetica

Bounding sup-norms of modular forms in terms of the level has been the focus of much recent study. In this work the sup-norm of a half-integral weight cusp form is bounded in terms of the level: we prove that | | y κ / 2 f ̃ | | ε , κ N 1 / 2 - 1 / 18 + ε | | y κ / 2 f ̃ | | L 2 for a modular form f̃ of level 4N and weight κ, a half-integer.

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