The Laplacian On Hyperbolic Riemann Surfaces And Maass Forms

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This thesis concerns the spectral theory of the Laplacian on Riemann surfaces of finite type, with emphasis on the quotients of the upper half plane by congruence subgroups. In a first part we show, following Otal, that on a Riemann surface M of genus g with n punctures there are at most 2g [-] 2 + n eigenvalues [lamda] with [lamda] [LESS-THAN OR EQUAL TO] 1/4. In a second part, we focus on arithmetic surfaces. This subject is treated by Maass in a paper that is difficult to read. We work out some examples of his construction of Maass forms.

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2015-08-17
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Laplacian; Rieamann surfaces; Maass forms
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Hubbard,John Hamal
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Muscalu,Florin Camil
Saloff-Coste,Laurent Pascal
Ramakrishna,Ravi Kumar
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Mathematics
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Ph. D., Mathematics
Degree Level
Doctor of Philosophy
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Government Document
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dissertation or thesis
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