This is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis. Extending the Rankin-Selberg method so as to apply it to the calculation of the Roelcke-Selberg decomposition of the product of two Eisenstein series, one lets Maass cusp-forms appear as residues of simple, Eisenstein-like, series. Other results, based on quantization theory, include a reinterpretation of the Lax-Phillips scattering theory for the automorphic wave equation, in terms of distributions on R2 automorphic with respect to the linear action...
This is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis. Extendi...
Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2002.
The subject of this book is the study of automorphic distributions, by which is meant distributions on R2 invariant under the linear action of SL(2, Z), and of the operators associated with such distributions under the Weyl rule of symbolic calculus.
Researchers and postgraduates interested in pseudodifferential analyis, the theory of non-holomorphic modular forms, and symbolic calculi will benefit from the clear exposition and new results and insights.
Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2002.
The subject of this book is the study of automorphic distributions, by w...
The n-dimensionalmetaplectic groupSp(n, R) is the twofoldcoverof the sympl- n n tic group Sp(n, R), which is the group of linear transformations ofX = R xR that preserve the bilinear (alternate) form x y ( ), ( )] =? x, ? + y, ? . (0. 1) ? ? 2 n There is a unitary representation of Sp(n, R)intheHilbertspace L (R ), called the metaplectic representation, the image of which is the groupof transformations generated by the following ones: the linear changes of variables, the operators of multiplication by exponentials with pure imaginary quadratic forms in the ex- nent, and the Fourier...
The n-dimensionalmetaplectic groupSp(n, R) is the twofoldcoverof the sympl- n n tic group Sp(n, R), which is the group of linear transformations ofX =...
(12) (4) Let ? be the unique even non-trivial Dirichlet character mod 12, and let ? be the unique (odd) non-trivial Dirichlet character mod 4. Consider on the line the distributions m (12) ? d (x)= ? (m)? x?, even 12 m?Z m (4) d (x)= ? (m)? x? . (1.1) odd 2 m?Z 2 i?x UnderaFouriertransformation, orundermultiplicationbythefunctionx ? e, the?rst(resp. second)ofthesedistributionsonlyundergoesmultiplicationbysome 24th (resp. 8th) root of unity. Then, consider the metaplectic representation Met, 2 a unitary representation in L (R) of the metaplectic group G, the twofold cover of the group G =...
(12) (4) Let ? be the unique even non-trivial Dirichlet character mod 12, and let ? be the unique (odd) non-trivial Dirichlet character mod 4. Conside...
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...
Pseudodifferential analysis, introduced in this book in a way adapted to the needs of number theorists, relates automorphic function theory in the ...
Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2002.
The subject of this book is the study of automorphic distributions, by which is meant distributions on R2 invariant under the linear action of SL(2, Z), and of the operators associated with such distributions under the Weyl rule of symbolic calculus.
Researchers and postgraduates interested in pseudodifferential analyis, the theory of non-holomorphic modular forms, and symbolic calculi will benefit from the clear exposition and new results and insights.
Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2002.
The subject of this book is the study of automorphic distributions, by w...
The main results of this book combine pseudo differential analysis with modular form theory. The methods rely for the most part on explicit spectral theory and the extended use of special functions. The starting point is a notion of modular distribution in the plane, which will be new to most readers and relates under the Radon transformation to the classical one of modular form of the non-holomorphic type. Modular forms of the holomorphic type are addressed too in a more concise way, within a general scheme dealing with quantization theory and elementary, but novel, representation-theoretic...
The main results of this book combine pseudo differential analysis with modular form theory. The methods rely for the most part on explicit spectral t...
