Buch, Englisch, Band 8, 300 Seiten, Format (B × H): 168 mm x 240 mm, Gewicht: 520 g
Buch, Englisch, Band 8, 300 Seiten, Format (B × H): 168 mm x 240 mm, Gewicht: 520 g
Reihe: Pseudo-Differential Operators
ISBN: 978-3-0348-0165-2
Verlag: Springer
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 Pi 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 Pi 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 E SL(2;Z), of some initial function, say in S(R2), is analyzed in detail. On Pi, a large class of new automorphic functions or measures is built in the same way: one of ist features lies in an interpretation, as a spectral density, of the restriction of the zeta function to any line within the critical strip. Several new ideas are far from being pushed to the end, and call for many possible generalizations, only hinted at.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
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.
