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 The Selberg Trace Formula for PSL 2 IR written by Dennis A. Hejhal and published by . This book was released on 1976 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 R 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 The Selberg Trace Formula for Psl 2 R written by Dennis A. Hejhal and published by . This book was released on 2014-09-01 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 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 Path Integrals Hyperbolic Spaces and Selberg Trace Formulae written by Christian Grosche and published by World Scientific. This book was released on 2013 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second edition, a comprehensive review is given for path integration in two- and three-dimensional (homogeneous) spaces of constant and non-constant curvature, including an enumeration of all the corresponding 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. Proposals concerning interbasis expansions for spheroidal coordinate systems are also given. In particular, the cases of non-constant curvature Darboux spaces are new in this edition. The volume also contains results on the numerical study of the properties of several integrable billiard systems in compact domains (i.e. rectangles, parallelepipeds, circles and spheres) in two- and three-dimensional flat and hyperbolic spaces. In particular, the discussions of integrable billiards in circles and spheres (flat and hyperbolic spaces) and in three dimensions are new in comparison to the first edition. In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, their use in mathematical physics and string theory, and some further results derived from the Selberg (super-) trace formula.

Download or read book Differential and Difference Equations written by Leonard C. Maximon and published by Springer. This book was released on 2016-04-18 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations - variation of constants, reduction of order, Laplace transforms and generating functions - bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green’s functions and the associated initial and boundary conditions is presented for differential and difference equations of both arbitrary and second order. A dictionary of difference equations with polynomial coefficients provides a unique compilation of second order difference equations obeyed by the special functions of mathematical physics. Appendices augmenting the text include, in particular, a proof of Cramer’s rule, a detailed consideration of the role of the superposition principal in the Green’s function, and a derivation of the inverse of Laplace transforms and generating functions of particular use in the solution of second order linear differential and difference equations with linear coefficients.

Download or read book Measure Theory Oberwolfach 1983 written by D. Kölzow and published by Springer. This book was released on 2006-11-14 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Weighted Inequalities and Degenerate Elliptic Partial Differential Equations written by E.W. Stredulinsky and published by Springer. This book was released on 2006-12-08 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Number Theory Noordwijkerhout 1983 written by H. Jager and published by Springer. This book was released on 2006-12-08 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Graph Theory Singapore 1983 written by K.M. Koh and published by Springer. This book was released on 2006-11-14 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probability Theory on Vector Spaces III written by D Szynal and published by Springer. This book was released on 2006-12-08 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Orders and their Applications written by Irving Reiner and published by Springer. This book was released on 2006-11-14 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions by numerous experts

Download or read book Probability Theory and Mathematical Statistics written by K. Ito and published by Springer. This book was released on 2006-11-15 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Equadiff 82 written by H. W. Knobloch and published by Springer. This book was released on 2007-01-05 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: