Share

Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi

2012-12-06 Mathematics
Download Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi PDF Online Free

Author :
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 784/5 ( reviews)

GET EBOOK


Book Synopsis Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi by : André Unterberger

Download or read book Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi written by André Unterberger. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms

2011-08-06 Mathematics
Download Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms PDF Online Free

Author :
Release : 2011-08-06
Genre : Mathematics
Kind : eBook
Book Rating : 661/5 ( reviews)

GET EBOOK


Book Synopsis Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms by : André Unterberger

Download or read book Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms written by André Unterberger. This book was released on 2011-08-06. Available in PDF, EPUB and Kindle. Book excerpt: 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 E 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.

Alternative Pseudodifferential Analysis

2008-11-14 Mathematics
Download Alternative Pseudodifferential Analysis PDF Online Free

Author :
Release : 2008-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 116/5 ( reviews)

GET EBOOK


Book Synopsis Alternative Pseudodifferential Analysis by : André Unterberger

Download or read book Alternative Pseudodifferential Analysis written by André Unterberger. This book was released on 2008-11-14. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces an entirely new pseudodifferential analysis on the line, the opposition of which to the usual (Weyl-type) analysis can be said to reflect that, in representation theory, between the representations from the discrete and from the (full, non-unitary) series, or that between modular forms of the holomorphic and substitute for the usual Moyal-type brackets. This pseudodifferential analysis relies on the one-dimensional case of the recently introduced anaplectic representation and analysis, a competitor of the metaplectic representation and usual analysis. Besides researchers and graduate students interested in pseudodifferential analysis and in modular forms, the book may also appeal to analysts and physicists, for its concepts making possible the transformation of creation-annihilation operators into automorphisms, simultaneously changing the usual scalar product into an indefinite but still non-degenerate one.

Pseudodifferential Operators with Automorphic Symbols

2015-06-22 Mathematics
Download Pseudodifferential Operators with Automorphic Symbols PDF Online Free

Author :
Release : 2015-06-22
Genre : Mathematics
Kind : eBook
Book Rating : 574/5 ( reviews)

GET EBOOK


Book Synopsis Pseudodifferential Operators with Automorphic Symbols by : André Unterberger

Download or read book Pseudodifferential Operators with Automorphic Symbols written by André Unterberger. This book was released on 2015-06-22. Available in PDF, EPUB and Kindle. Book excerpt: 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 concepts.

Pseudodifferential Methods in Number Theory

2018-07-16 Mathematics
Download Pseudodifferential Methods in Number Theory PDF Online Free

Author :
Release : 2018-07-16
Genre : Mathematics
Kind : eBook
Book Rating : 078/5 ( reviews)

GET EBOOK


Book Synopsis Pseudodifferential Methods in Number Theory by : André Unterberger

Download or read book Pseudodifferential Methods in Number Theory written by André Unterberger. This book was released on 2018-07-16. Available in PDF, EPUB and Kindle. Book excerpt: Classically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic. The operators which make up the main subject of the book can be characterized in terms of congruence arithmetic. They enjoy a Eulerian structure, and are applied to the search for new conditions equivalent to the Riemann hypothesis. These consist in the validity of certain parameter-dependent estimates for a class of Hermitian forms of finite rank. The Littlewood criterion, involving sums of Möbius coefficients, and the Weil so-called explicit formula, which leads to his positivity criterion, fit within this scheme, using in the first case Weyl's pseudodifferential calculus, in the second case Fuchs'. The book should be of interest to people looking for new possible approaches to the Riemann hypothesis, also to new perspectives on pseudodifferential analysis and on the way it combines with modular form theory. Analysts will have no difficulty with the arithmetic aspects, with which, save for very few exceptions, no previous acquaintance is necessary.

You may also like...