Download or read book An Approach to the Selberg Trace Formula via the Selberg Zeta Function written by Jürgen Fischer and published by Springer. This book was released on 2006-11-15 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Notes give a direct approach to the Selberg zeta-function for cofinite discrete subgroups of SL (2,#3) acting on the upper half-plane. The basic idea is to compute the trace of the iterated resolvent kernel of the hyperbolic Laplacian in order to arrive at the logarithmic derivative of the Selberg zeta-function. Previous knowledge of the Selberg trace formula is not assumed. The theory is developed for arbitrary real weights and for arbitrary multiplier systems permitting an approach to known results on classical automorphic forms without the Riemann-Roch theorem. The author's discussion of the Selberg trace formula stresses the analogy with the Riemann zeta-function. For example, the canonical factorization theorem involves an analogue of the Euler constant. Finally the general Selberg trace formula is deduced easily from the properties of the Selberg zeta-function: this is similar to the procedure in analytic number theory where the explicit formulae are deduced from the properties of the Riemann zeta-function. Apart from the basic spectral theory of the Laplacian for cofinite groups the book is self-contained and will be useful as a quick approach to the Selberg zeta-function and the Selberg trace formula.
Download or read book The Selberg trace formula for PSL 2 IR written by Dennis A. Hejhal and published by . This book was released on 2014-01-15 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Local Analysis of Selberg s Trace Formula written by A. Good and published by . This book was released on 2014-01-15 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on the Arthur Selberg Trace Formula written by Stephen S. Gelbart and published by American Mathematical Soc.. This book was released on 1996 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Arthur-Selberg trace formula is an equality between two kinds of traces: the geometric terms given by the conjugacy classes of a group and the spectral terms given by the induced representations. In general, these terms require a truncation in order to converge, which leads to an equality of truncated kernels. The formulas are difficult in general and even the case of $GL$(2) is nontrivial. The book gives proof of Arthur's trace formula of the 1970s and 1980s, with special attention given to $GL$(2). The problem is that when the truncated terms converge, they are also shown to be polynomial in the truncation variable and expressed as ``weighted'' orbital and ``weighted'' characters. In some important cases the trace formula takes on a simple form over $G$. The author gives some examples of this, and also some examples of Jacquet's relative trace formula. This work offers for the first time a simultaneous treatment of a general group with the case of $GL$(2). It also treats the trace formula with the example of Jacquet's relative formula. Features: Discusses why the terms of the geometric and spectral type must be truncated, and why the resulting truncations are polynomials in the truncation of value $T$. Brings into play the significant tool of ($G, M$) families and how the theory of Paley-Weiner is applied. Explains why the truncation formula reduces to a simple formula involving only the elliptic terms on the geometric sides with the representations appearing cuspidally on the spectral side (applies to Tamagawa numbers). Outlines Jacquet's trace formula and shows how it works for $GL$(2).
Download or read book The Selberg Trace Formula for PSL 2 R written by Dennis A. Hejhal and published by Springer. This book was released on 2006-11-14 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Selberg Arthur Trace Formula written by Salahoddin Shokranian and published by Springer. This book was released on 2006-11-14 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book based on lectures given by James Arthur discusses the trace formula of Selberg and Arthur. The emphasis is laid on Arthur's trace formula for GL(r), with several examples in order to illustrate the basic concepts. The book will be useful and stimulating reading for graduate students in automorphic forms, analytic number theory, and non-commutative harmonic analysis, as well as researchers in these fields. Contents: I. Number Theory and Automorphic Representations.1.1. Some problems in classical number theory, 1.2. Modular forms and automorphic representations; II. Selberg's Trace Formula 2.1. Historical Remarks, 2.2. Orbital integrals and Selberg's trace formula, 2.3.Three examples, 2.4. A necessary condition, 2.5. Generalizations and applications; III. Kernel Functions and the Convergence Theorem, 3.1. Preliminaries on GL(r), 3.2. Combinatorics and reduction theory, 3.3. The convergence theorem; IV. The Ad lic Theory, 4.1. Basic facts; V. The Geometric Theory, 5.1. The JTO(f) and JT(f) distributions, 5.2. A geometric I-function, 5.3. The weight functions; VI. The Geometric Expansionof the Trace Formula, 6.1. Weighted orbital integrals, 6.2. The unipotent distribution; VII. The Spectral Theory, 7.1. A review of the Eisenstein series, 7.2. Cusp forms, truncation, the trace formula; VIII.The Invariant Trace Formula and its Applications, 8.1. The invariant trace formula for GL(r), 8.2. Applications and remarks
Download or read book The Selberg Trace Formula III Inner Product Formulae Initial Considerations written by M. Scott Osborne and published by American Mathematical Soc.. This book was released on 1983 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this memoir, we lay the foundations for the study of inner product formulae, one of the key technical preliminaries in the derivation of the Selberg trace formula.
Download or read book On the Stabilization of the Trace Formula written by Laurent Clozel and published by International Pressof Boston Incorporated. This book was released on 2011 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lecture Notes in Mathematics written by and published by . This book was released on 1964 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Selberg Trace Formula for PSL 2 R written by Dennis A. Hejhal and published by Springer. This book was released on 2006-11-15 with total page 815 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Path Integrals Hyperbolic Spaces And Selberg Trace Formulae written by Christian Grosche and published by World Scientific. This book was released on 1996-02-29 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, a comprehensive review is given for path integration in two- and three-dimensional homogeneous spaces of constant curvature, including an enumeration of all coordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation.In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, and their use in mathematical physics and quantum chaos.The volume also contains results on the study of the properties of a particular integrable billiard system in the hyperbolic plane, a proposal concerning interbasis expansions for spheroidal coordinate systems in four-dimensional Euclidean space, and some further results derived from the Selberg (super-) trace formula.
Download or read book The Selberg Trace Formula for PSL 2 R n written by Isaac Y. Efrat and published by American Mathematical Soc.. This book was released on 1987 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: We evaluate the Selberg trace formula for all discrete, irreducible, cofinite subgroups of PSL2 ([double-struck capital]R)[italic superscript]n. In particular, this involves studying the spectral theory of the fundamental domain, and the analysis of the appropriate Eisenstein series. A special role is played by the Hilbert modular groups, both because of their relation to the general case, stemming from a rigidity theorem, and their inherent algebraic number theoretic interest.
Download or read book Number Theory Trace Formulas and Discrete Groups written by Atle Selberg and published by . This book was released on 1989 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number Theory, Trace Formulas and Discrete Groups.
Download or read book Traces of Hecke Operators written by Andrew Knightly and published by American Mathematical Soc.. This book was released on 2006 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fourier coefficients of modular forms are of widespread interest as an important source of arithmetic information. In many cases, these coefficients can be recovered from explicit knowledge of the traces of Hecke operators. The original trace formula for Hecke operators was given by Selberg in 1956. Many improvements were made in subsequent years, notably by Eichler and Hijikata. This book provides a comprehensive modern treatment of the Eichler-Selberg/Hijikata trace formulafor the traces of Hecke operators on spaces of holomorphic cusp forms of weight $\mathtt{k >2$ for congruence subgroups of $\operatorname{SL 2(\mathbf{Z )$. The first half of the text brings together the background from number theory and representation theory required for the computation. Thisincludes detailed discussions of modular forms, Hecke operators, adeles and ideles, structure theory for $\operatorname{GL 2(\mathbf{A )$, strong approximation, integration on locally compact groups, the Poisson summation formula, adelic zeta functions, basic representation theory for locally compact groups, the unitary representations of $\operatorname{GL 2(\mathbf{R )$, and the connection between classical cusp forms and their adelic counterparts on $\operatorname{GL 2(\mathbf{A )$. Thesecond half begins with a full development of the geometric side of the Arthur-Selberg trace formula for the group $\operatorname{GL 2(\mathbf{A )$. This leads to an expression for the trace of a Hecke operator, which is then computed explicitly. The exposition is virtually self-contained, withcomplete references for the occasional use of auxiliary results. The book concludes with several applications of the final formula.
Download or read book The Selberg Trace Formula for PSL 2 IR written by Dennis A. Hejhal and published by Springer. This book was released on 1976 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Selberg Trace Formula for Psl 2 Tr Volume 2 written by Dennis A. Hejhal and published by . This book was released on 1983 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operator Theory Operator Algebras and Their Interactions with Geometry and Topology written by Raul E Curto and published by Springer Nature. This book was released on 2020-12-12 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas’ students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.
