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Beyond the Stars
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The Theory of Eisenstein Systems
The Theory of Eisenstein Systems
Scattering Operator, Eisenstein Series, Inner Product Formula and ``Maass-Selberg'' Relations for Kleinian Groups
In this memoir we have introduced and studied the scattering operator and the Eisenstein series and we have formulated and proved the inner product formula and the "Maass-Selberg" relations for Kleinian groups.
The Meromorphic Continuation and Functional Equations of Cuspidal Eisenstein Series for Maximal Cuspidal Subgroups
We carry out, in the context of an algebraic group and an arithmetic subgroup, an idea of Selberg for continuing Eisenstein series. It makes use of the theory of integral operators. The meromorphic continuation and functional equation of an Eisenstein series constructed with a cusp form on the Levi component of a rank one cuspidal subgroup are established.
Eisenstein Series and Applications
Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas which do not usually interact with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series. The central theme of the exposition focuses on the common structural properties of Eisenstein series occurring in many related applications.
