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Autor Unterberger, André. author.

Título Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms [electronic resource] / by André Unterberger.

Publicación Basel : Springer Basel, 2011.
Descripción física VIII, 300p. online resource.
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Colección Pseudo-Differential Operators, Theory and Applications ; 8
Pseudo-Differential Operators, Theory and Applications ; 8
Springer eBooks. Mathematics and Statistics
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Contiene: Introduction -- The Weyl calculus -- The Radon transformation and applications -- Automorphic functions and automorphic distributions -- A class of Poincaré series -- Spectral decomposition of the Poincaré summation process -- The totally radial Weyl calculus and arithmetic -- Should one generalize the Weyl calculus to an adelic setting? -- Index of notation -- Subject Index -- Bibliography.
Resumen: Pseudodifferential analysis, introduced in this book in a way adapted to the needs of number theorists, relates automorphic function theory in the hyperbolic half-plane Π to automorphic distribution theory in the plane. Spectral-theoretic questions are discussed in one or the other environment: in the latter one, the problem of decomposing automorphic functions in Π according to the spectral decomposition of the modular Laplacian gives way to the simpler one of decomposing automorphic distributions in R2 into homogeneous components. The Poincaré summation process, which consists in building automorphic distributions as series of g-transforms, for g Î SL(2;Z), of some initial function, say in S(R2), is analyzed in detail. On Π, a large class of new automorphic functions or measures is built in the same way: one of its features lies in an interpretation, as a spectral density, of the restriction of the zeta function to any line within the critical strip. The book is addressed to a wide audience of advanced graduate students and researchers working in analytic number theory or pseudo-differential analysis.
Materia Mathematics.
Operator theory.
Number theory.
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Number Theory.
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Operator Theory.
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Autor secundario SpringerLink (Online service)
En Springer eBooks
OTRO SOPORTE Printed edition: 9783034801652
ISBN 9783034801669 978-3-0348-0166-9
ISBN/ISSN 10.1007/978-3-0348-0166-9 doi