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A local large sieve inequality for cusp forms

Jonathan Wing Chung Lam (2014)

Journal de Théorie des Nombres de Bordeaux

We prove a large sieve type inequality for Maass forms and holomorphic cusp forms with level greater or equal to one and of integral or half-integral weight in short interval.

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.

From pseudodifferential analysis to modular form theory

André Unterberger (1999)

Journées équations aux dérivées partielles

Taking advantage of methods originating with quantization theory, we try to get some better hold - if not an actual construction - of Maass (non-holomorphic) cusp-forms. We work backwards, from the rather simple results to the mostly devious road used to prove them.

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