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The Heat Kernel and Theta Inversion on SL2(C) by Jay Jorgenson, Serge Lang

The Heat Kernel and Theta Inversion on SL2(C)


Part of the Springer Monographs in Mathematics Series


The Heat Kernel and Theta Inversion on SL2(C) by Jay Jorgenson, Serge Lang

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.


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)

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Book Info

Publication date

12th February 2010


Jay Jorgenson, Serge Lang

More books by Jay Jorgenson, Serge Lang
Author 'Like for Like'


Springer-Verlag New York Inc.


319 pages


Number theory
Groups & group theory
Calculus & mathematical analysis



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