The Heat Kernel and Theta Inversion on SL2(C) / Edition 1

The Heat Kernel and Theta Inversion on SL2(C) / Edition 1

by Jay Jorgenson, Serge Lang
     
 

ISBN-10: 0387380310

ISBN-13: 9780387380315

Pub. Date: 10/15/2008

Publisher: Springer New York

The present monograph devlops the fundamental ideas and relults surronding heat kenels, spectral theory, and regularized traces associated the full modular group action on SL2(C) through spherical transform, from which one manifestation of the heat kernel on quotient spaces is obtained through group perodization. Fron a different point of view, one

…  See more details below

Overview

The present monograph devlops the fundamental ideas and relults surronding heat kenels, spectral theory, and regularized traces associated the full modular group action on SL2(C) through spherical transform, from which one manifestation of the heat kernel on quotient spaces is obtained through group perodization. Fron a different point of view, one constructs the heat kernel on the group space using an eignfuction, or spectral, expansion, which then leads to a theta function and a theta inbversion formula by equating the two realizations of the heat kernel on the quotient space. The trace of the heat kernel diverges, which naturally leads to a regularization of the trace by studying Eisenstein series on the eigenfunction side and the cuspidal elements on the group periodization side. By focusing on the case of Sl2 (z[i]) acting on SL2(C), the authors are able to emphasize the importance of specific examples of the general theory of the general Selgerg trace formula and uncover the second step in their envisioned "ladder" of geometrically defined zet functions, where each conjectured step would include lower level zeta functions as factors in functional equations.

Read More

Product Details

ISBN-13:
9780387380315
Publisher:
Springer New York
Publication date:
10/15/2008
Series:
Springer Monographs in Mathematics Series
Edition description:
2008
Pages:
319
Product dimensions:
6.30(w) x 9.30(h) x 0.80(d)

Table of Contents


Pt. I Gaussians, Spherical Inversion, and the Heat Kernel
1 Spherical Inversion on SL[subscript 2](C) 13
2 The Heat Gaussian and Heat Kernel 45
3 QED, LEG, Transpose, and Casimir 67 Pt. II Enter [Gamma]: The General Trace Formula
4 Convergence and Divergence of the Selberg Trace 85
5 The Cuspidal and Noncuspidal Traces 97 Pt. III The Heat Kernel on [Gamma]\G/K
6 The Fundamental Domain 117
7 [Gamma]-Periodization of the Heat Kernel 135
8 Heat Kernel Convolution on L[superscript 2][subscript cusp] ([Gamma]\G/K) 151 Pt. IV Fourier-Eisenstein Eigenfunction Expansions
9 The Tube Domain for [Gamma][infinity] 167
10 The [Gamma][subscript U]\U-Fourier Expansion of Eisenstein Series 191
11 Adjointness Formula and the [Gamma]\G-Eigenfunction Expansion 223 Pt. V The Eisenstein - Cuspidal Affiar
12 The Eisenstein Y-Asymptotics 243
13 The Cuspidal Trace Y-Asymptotics 261
14 Analytic Evaluations 287 References 311 Index 317

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >