Overview
The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, the approach taken here is to begin with the heat kernel on SL(2,C) associated to the invariant Laplacian, which is derived using spherical inversion. The heat kernel on the quotient space SL(2,Z[i])\SL(2,C) is arrived at through periodization, and further expanded in an eigenfunction expansion. A theta inversion formula is obtained by studying the trace of the heat kernel. Following the author's previous work, the inversion formula then leads to zeta functions through the Gauss transform.
Full Product Details
Author: Jay Jorgenson ,
Serge Lang
Publisher: Springer-Verlag New York Inc.
Imprint: Springer-Verlag New York Inc.
Edition: Softcover reprint of hardcover 1st ed. 2008
Dimensions:
Width: 15.50cm
, Height: 1.70cm
, Length: 23.50cm
Weight: 0.510kg
ISBN: 9781441922823
ISBN 10: 1441922822
Pages: 319
Publication Date: 19 November 2010
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Out of print, replaced by POD
We will order this item for you from a manufatured on demand supplier.
Reviews
From the reviews: The book under review ! provides an introduction to the general theory of semisimple or reductive groups G, with symmetric space G/K (K maximal compact). ! It is ! meant for experienced insiders, even as the presentation of the material is excellent and accessible. A well-prepared graduate student would do well with this book. More experienced analytic number theorists will find it enjoyable and spellbinding. ! I heartily recommend to other analytic number theorists of a similar disposition. (Michael Berg, MAA Online, December, 2008) This book is part of a program of the authors to develop a systematic theory of theta and zeta functions on homogeneous spaces, using techniques of harmonic analysis and, in particular, heat kernels. ! the book includes many details that would likely have been left for the reader to work out by her/himself in a more streamlined monograph. ! all in all, an enjoyable book to read. (Fredrik Stromberg, Zentralblatt MATH, Vol. 1192, 2010)
From the reviews: The book under review ! provides an introduction to the general theory of semisimple or reductive groups G, with symmetric space G/K (K maximal compact). ! It is ! meant for experienced insiders, even as the presentation of the material is excellent and accessible. A well-prepared graduate student would do well with this book. More experienced analytic number theorists will find it enjoyable and spellbinding. ! I heartily recommend to other analytic number theorists of a similar disposition. (Michael Berg, MAA Online, December, 2008)
From the reviews: The book under review ... provides an introduction to the general theory of semisimple or reductive groups G, with symmetric space G/K (K maximal compact). ... It is ... meant for experienced insiders, even as the presentation of the material is excellent and accessible. A well-prepared graduate student would do well with this book. More experienced analytic number theorists will find it enjoyable and spellbinding. ... I heartily recommend to other analytic number theorists of a similar disposition. (Michael Berg, MAA Online, December, 2008) This book is part of a program of the authors to develop a systematic theory of theta and zeta functions on homogeneous spaces, using techniques of harmonic analysis and, in particular, heat kernels. ... the book includes many details that would likely have been left for the reader to work out by her/himself in a more streamlined monograph. ... all in all, an enjoyable book to read. (Fredrik Stroemberg, Zentralblatt MATH, Vol. 1192, 2010)
