Springer Monographs in Mathematics

The Heat Kernel and Theta Inversion on SL2(C)

Authors: Jorgenson, Jay, Lang, Serge

  • Contains new research and results
  • Simplifies the development of the trace formula and theta inversion by using the heat kernel
  • One of the co-authors, Serge Lang, was the most prolific author of recent times in this research area
  • Comprehensive and self-contained treatment of the subject
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eBook $149.00
price for USA (gross)
  • ISBN 978-0-387-38032-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-0-387-38031-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-1-4419-2282-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

The present monograph develops the fundamental ideas and results surrounding heat kernels, spectral theory, and regularized traces associated to the full modular group acting on SL2(C). The authors begin with the realization of the heat kernel on SL2(C) through spherical transform, from which one manifestation of the heat kernel on quotient spaces is obtained through group periodization. From a different point of view, one constructs the heat kernel on the group space using an eigenfunction, or spectral, expansion, which then leads to a theta function and a theta inversion 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 Selberg trace formula and uncover the second step in their envisioned "ladder" of geometrically defined zeta functions, where each conjectured step would include lower level zeta functions as factors in functional equations.

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 Strömberg, Zentralblatt MATH, Vol. 1192, 2010)


Table of contents (15 chapters)

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-0-387-38032-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-0-387-38031-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-1-4419-2282-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Heat Kernel and Theta Inversion on SL2(C)
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2008
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-38032-2
DOI
10.1007/978-0-387-38032-2
Hardcover ISBN
978-0-387-38031-5
Softcover ISBN
978-1-4419-2282-3
Series ISSN
1439-7382
Edition Number
1
Number of Pages
X, 319
Topics