Pseudodifferential analysis, automorphic distributions in the plane and modular forms
著者
書誌事項
Pseudodifferential analysis, automorphic distributions in the plane and modular forms
（Pseudo-differential operators : theory and applications / managing editor, M.W. Wong, v. 8）
Birkhäuser, c2011
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注記
Includes bibliographical references (p. [295]-299) and index
内容説明・目次
内容説明
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 R2 into homogeneous components. The Poincare 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 , 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.
目次
Introduction.- The Weyl calculus.- The Radon transformation and applications.- Automorphic functions and automorphic distributions.- A class of Poincare series.- Spectral decomposition of the Poincare 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.
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