Unterberger Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms
1. Auflage 2011
ISBN: 978-3-0348-0166-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 300 Seiten, Web PDF
Reihe: Pseudo-Differential Operators
ISBN: 978-3-0348-0166-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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 ? 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 ? according to the spectral decomposition of the modular Laplacian gives way to the simpler one of decomposing automorphic distributions in R into homogeneous components. The Poincaré summation process, which consists in building automorphic distributions as series of g-transforms, for g E SL(2;Z), of some initial function, say in S(R), is analyzed in detail. On ?, 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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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.
