Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms write by André Unterberger. This book was released on 2011-08-06. Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms available in PDF, EPUB and Kindle. 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.
Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms
Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms write by André Unterberger. This book was released on 2011-08-26. Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms available in PDF, EPUB and Kindle. 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.
Pseudodifferential Operators with Automorphic Symbols
Pseudodifferential Operators with Automorphic Symbols - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Pseudodifferential Operators with Automorphic Symbols write by André Unterberger. This book was released on 2015-06-22. Pseudodifferential Operators with Automorphic Symbols available in PDF, EPUB and Kindle. 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
Pseudodifferential Methods in Number Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Pseudodifferential Methods in Number Theory write by André Unterberger. This book was released on 2018-07-16. Pseudodifferential Methods in Number Theory available in PDF, EPUB and Kindle. 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.
Operator Algebras, Toeplitz Operators and Related Topics
Operator Algebras, Toeplitz Operators and Related Topics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Operator Algebras, Toeplitz Operators and Related Topics write by Wolfram Bauer. This book was released on 2020-09-01. Operator Algebras, Toeplitz Operators and Related Topics available in PDF, EPUB and Kindle. This book features a collection of up-to-date research papers that study various aspects of general operator algebra theory and concrete classes of operators, including a range of applications. Most of the papers included were presented at the International Workshop on Operator Algebras, Toeplitz Operators, and Related Topics, in Boca del Rio, Veracruz, Mexico, in November 2018. The conference, which was attended by more than 30 leading experts in the field, was held in celebration of Nikolai Vasilevski’s 70th birthday, and the contributions are dedicated to him.
