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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The $ L\sp{2}$-norm of Maass wave functions


Author: Robert A. Smith
Journal: Proc. Amer. Math. Soc. 82 (1981), 179-182
MSC: Primary 10D12
DOI: https://doi.org/10.1090/S0002-9939-1981-0609646-7
MathSciNet review: 609646
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Abstract: Let $ D$ denote the fundamental domain for the full modular group. Suppose that $ f \in {L^2}(D)$ satisfies the wave equation $ \Delta f = \lambda f$, where $ \Delta $ is the noneuclidean Laplacian, and further, assume that $ f$ is a common eigenfunction for all the Hecke operators. Then upper and lower bounds for the $ {L^2}$-norm of $ f$ are determined which depend only on $ \lambda $ and the first Fourier coefficient of $ f$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0609646-7
Keywords: Maass wave function, Laplacian, Hecke operator
Article copyright: © Copyright 1981 American Mathematical Society